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"COOPER  ON  BELTING." 

A  TREATISE  ON  THE  USE  OF  BELTING  FOB  THE  TRANSMISSION  OF  POWER. 
With  numerous  illustrations  of  approved  and  actual  methods  of  arrang- 
ing Main  Driving  and  Quarter  Twist  Belts,  and  of  Belt  Fastenings.  Ex- 
amples and  Rules  in  great  number  for  exhibiting  and  calculating  the  size 
and  driving  power  of  Belts.  Plain,  Particular,  and  Practical  Directions 
for  the  Treatment,  Care,  and  Management  of  Belts.  Descriptions  of 
many  varieties  of  Beltings,  together  with  chapters  on  the  Transmission  of 
Power  by  Ropes ;  by  Iron  and  Wood  Frictional  Gearing ;  on  the  Strength 
of  Belting  Leather ;  and  on  the  Experimental  Investigations  of  Morin, 
Briggs,  and  others  for  determining  the  Friction  of  Belts  under  different 
tensions,  which  are  presented  clearly  and  fully,  with  the  text  and  tables 
unabridged. 

By  JOHN  H.  COOPER,  M.E. 

Second.   Ed.     One   vol.,   demi   octavo.     Cloth,   $3.5O. 

The  Publishers  will  send  copies  by  mail,  postage  prepaid,  on  receipt  of  price, 


WHAT  THEY  SAY  OF  IT. 

"  It  contains  a  great  deal  of  much-needed  information.''— BROWN  &  ALLEN,  N.  Y. 
"A  useful  and  instructive  volume,  typographically  creditable."— JAS.  CHRISTIE,  Phil- 

"  It  collects  in  the  simplest  manner  the  opinions  of  practical  and  theoretical  men."— 
R.  BRIGGS,  M.  E.,  Philadelphia. 

"  It  contains  everything  that  need  be  said  on  this  important  subject."— H.  HOWSON,  M. 
E.,  Philadelphia. 

"  We  confidently  welcome  it  as  the  standard  treatise  on  belting."— POLYTECHNIC  RE- 
VIEW. Philadelphia. 

"  You  have  studied  clearness  instead  of  mystification."— J.  C.  TRAUTWINE,  C.  E.,  Philada. 

"  More  to  be  found  in  your  book  upon  this  subject  than  in  all  the  world  beside."— Prof 
J.  E.  SWEET,  Cornell  University. 

"  A  thorough  and  complete  treatise  on  the  subject  of  belting."— SCIENTIFIC  AMERICAN, 

"  There  is  also  much  original  matter  never  before  printed." — HERALD  AND  FREE  PRESS, 
Norristown,  Pa. 

"  This  work  is  exhaustive  in  character,  and  creditable  to  author  and  publishers."— AM. 
R.  R.  JOURNAL,  N.  Y. 

"  Fully  illustrated  in  every  respect,  and  a  most  valuable  contribution  to  technical  lit- 
erature. — LEFFEL'S  MILLING  NEWS,  Springfield,  O. 

"  A  complete  treatise,  embracing  every  variety  of  transmitting  power  by  belts  and 
ropes."— J.  W.  NYSTROM,  M.  E.,  Philadelphia. 

"  Written  in  the  plainest  language ;  easiest  book  to  understand  I  ever  read."— G.  V. 
CRIPPS,  Philadelphia. 

"  An  encyclopedia,  eighty  illustrations,  and  numerous  tables  of  great  value." — N. 
AMERICAN,  Philadelphia. 

"  Comprehensive,  practical  work,  the  careful  study  of  which  would  save  millions  of 
dollars  annually.' —E.  S.  WICKLIN,  Millwright,  Wis. 

"  This  work  has  a  good  index ;  use  of  belting  explained  in  clear  language."— PRESS, 
Philadelphia. 

"An  eminently  practical  work,  subject  treated  with  fulness  and  perspicuity."— 
PRINTERS'  CIRCULAR,  Philadelphia. 

"  The  mass  of  facts  and  figures  presented  cover  every  point  of  theory  and  practice.  It 
includes  information  from  every  available  source;  a  valuable  assistant."— N.  W.  LUM- 
BERMAN, Chicago,  111. 

"  I  consider  it  a  most  valuable  contribution  to  technical  literature  "—Prof.  A.  BEARDS- 
LEY,  Swarthmore  College,  Pa. 

"  A  very  admirable  and  exhaustive  treatise.' WHon.  ELLIS  SPEAR,  Commissioner  of  Pat- 
ents, Washington,  D.  C. 

"  '  Use  of  Belting'  supplies  a  want  long  felt  by  all  mechanical  engineers."— TAWS  & 
HARTMAN,  Engineers,  Philadelphia. 

"  The  need  for  such  a  book  as  this  has  long  been  manifest."— VAN  NOSTRAND'S  ECLEC- 
TIC MAG.,  N.  Y. 

"  The  most  complete  collection  of  rules,  tables,  and  statistics  upon  the  use  of  belts  now 
in  print." — JOURNAL  OF  FRANKLIN  INSTITUTE,  Philadelphia. 

"  No  intelligent  man  can  read  your  book  carefully  without  informing  himself  pretty 
thoroughly  as  to  what  can  actually  be  done  with  belting."— SAM' L  WEBBER,  M.  E.  Man- 
chester, N.  H. 


TREATISE 


ON  THE 


USE  OF  BELTING 


FOR  THE 


TRANSMISSION  OF  POWER. 


JOHN  H.  COOPER, 

MECHANICAL  ENGINEER. 


SECOND    EDITION 


PHILADELPHIA: 
E.CLAXTON  &  COMPANY, 

LONDON :  E.  &  F.  N.  SPON,  16  CHARING  CROSS. 
1883. 


44" 


-AN 


Entered,  according  to  Act  of  Congress,  in  the  year  1877,  by 

CLAXTON,  REMSEN  &  HAFFELFINGER, 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


^* 

J.    PAGAN    &    SON,  *^| 

BLECTROTYPERS,    PHILAD'A. 


DORNAN,    PRINTER, 
PHILADELPHIA. 


PREFACE 

TO  THE  SECOND  EDITION. 


THE  demand  for  a  second  edition  of  Use  of  Belting  offers  occasion  to  me  to 
thank  my  readers  and  critics  for  the  very  favorable  opinions  entertained 
regarding  my  work,  and  for  the  good  words  expressed  in  its  behalf. 

Of  the  many  full  and  favorable  notices  concerning  the  book,  there  occurs  one 
statement — friendly  and  true,  I  believe — but  about  which  I  deem  necessary  cer- 
tain explanations  in  justification  of  the  object  I  had  in  view  when  placing  this 
work  before  the  public. 

The  statement  referred  to  exists  in  a  paper  on  a  "  Formula  for  the  Horse- 
Power  of  Leather  Belts,"  read  at  the  Hartford  meeting  of  the  American  Society 
of  Mechanical  Engineers,  held  in  May,  1881,  of  which  the  following  is  the  sub- 
stance and  text :  In  "  a  recent  book  on  the  Use  of  Belting,  I  found  a  large  and 
valuable  collection  of  matter  on  the  subject,  but  no  attempt  was  made  to  assimi- 
late the  same." 

I  am  pleased  to  know  that  the  book  is  found  on  perusal  by  intelligent  readers, 
not  only  to  be  full  of  valuable  matter,  but  that  it  also  supplies  many  helps  in  the 
shape  of  experimental  data  and  practical  working  of  belts. 

As  already  stated  in  Use  of  Belting,  my  whole  aim  in  producing  it  was  to  pre- 
sent the  largest  array  of  facts  and  figures  consistent  with  accuracy  and  in  har- 
mony with  best  use,  and  not  to  reduce  the  particulars  of  performance  to  one  rule 
or  statement.  A  square  inch  of  paper  holds  area  sufficient  for  a  horse-power 
rule  of  belt  performance,  but  a  large  book  is  necessary  to  tell  the  whole  story  of 
the  use  of  belting. 

Assimilation  is  impossible  where  the  modifying  circumstances  exist  in  such 
great  number  and  variety  as  they  do  under  which  belts  act. 

If  we  assume  that  the  various  published  rules  for  ascertaining  the  horse-power 
of  a  belt  represent  the  expressed  assimilations  of  the  data  collated  by  the  author 
of  each,  we  shall  have  a  considerable  group  of  fairly  formulated  statements ;  but 
how  near  to  the  average  truth  they  will  approach  can  best  be  ascertained  by 
reference  to  the  rules  for  belts  already  given  in  Use  of  Belting. 

In  the  making  of  many  rules,  too  much  stress  is  placed  upon  niceties  of  mathe- 
matical expression,  to  the  utter  disregard  of  the  many  disturbing  conditions  of 
practice  and  the  persistent  facts  of  working.  What  does  it  avail  with  formulated 
fine-spun,  if,  for  example,  the  length  and  tightness  of  belts,  the  angle  at  which 
they  are  running,  and  the  character  of  the  adhesives  applied,  are  left  out  of  con- 
sideration by  the  rule,  when  we  know  that  any  one  of  these  conditions  will 
greatly  affect  the  driving  power  of  a  belt  ? 


PREFACE    TO    THE    SECOND    EDITION. 

Adhesion  is  a  greater  fulcrum  to  the  driving  power  than  friction ;  each  is  sub- 
ject to  its  own  laws ;  the  law  of  this  has  been  largely  investigated  and  relied 
upon,  but  for  that  there  seems  to  be  no  written  law  or  certainty  of  result,  yet 
when  friction  fails,  the  rule  is — apply  an  adhesive. 

I  believe  the  largest  presentation  of  facts  and  conditions  affords  the  best 
material  for  study  of  the  subject.  I  have  no  fears  for  good  proportions  and 
best  running  conditions  in  the  hands  of  the  intelligent  mechanic,  if  he  is  pro- 
vided with  the  results  of  reliable  experiments,  and  studies  them  in  connection 
with  the  circumstances  under  which  they  were  made. 

On  page  ix  of  the  Introduction,  I  have  given  an  outline  of  reliable  data  for 
the  guidance  of  the  practical  engineer  who  wishes  to  have  knowledge  of  a  fair 
average  of  belt  strength,  and  of  the  force  which  belts  are  capable  of  transmitting 
in  the  ordinary  way  of  using  them ;  and  on  page  xi  I  have  given  some  of  the 
conditions  to  be  fulfilled  in  the  use  of  belts  in  order  to  get  best  service  from  them. 

It  is  safe  to  say  that  no  better  assimilation  of  belt  data  can  be  made  than  that 
already  presented  in  these  pages.  More  conditions  and  variety  of  conditions, 
when  discovered,  will  be  added  to  this  considerable  list ;  but  the  last  deduction, 
when  all  the  facts  are  in,  will  give  to  the  practical  man  for  use  a  simple  state- 
ment, something  like  this:  aflat  leather  belt  of  the  usual  make,  one  inch  in  width, 
will  transmit  a  force  of  say  55  Ibs.  at  any  ordinary  velocity,  running  freely  on  smooth- 
faced pulleys. 

An  easily  made  experiment  will  prove  that  such  a  belt  will  transmit  a  force 
of  100  Ibs.,  or  even  more,  but  for  long  unfailing  service  the  amount  named  is  not 
far  from  the  best  practice.  One  can  easily  see  and  understand  that  a  unit  of  this 
character,  like  a  known  tensile  strength  of  good  wrought-iron  per  square  inch 
of  section,  is  a  factor  of  almost  universal  application,  and  is  in  harmony  with 
the  use  of  belting. 

There  are  theoretical  crotchets  in  many  books ;  nevertheless,  rules  for  belting 
should  be  "  practical  as  far  as  possible,  theoretical  as  far  as  necessary,"  and  yet 
it  will  ever  be  true  on  test,  that  each  material  gives  its  own  figures,  which  can 
only  be  known  to  those  who  lay  a  hand  to  the  practical  side  of  the  subject  as 
well  as  a  head  to  the  principles  which  govern  the  movements. 

Mention  is  made  of  a  difference  between  Adhesion  and  Friction.  It  may  be 
said,  in  general,  that  friction  is  in  proportion  to  the  weight,  but  independent  of 
the  surface  exposed  to  the  sliding  action ;  adhesion,  on  the  other  hand,  is  in 
proportion  to  the  extent  of  surface  and  to  the  nature  of  the  adhesive. 

Either  or  both  of  these  may  act  with  running  belts.  For  many  reasons,  there- 
fore, closer  observation  and  comparisons  of  them  with  more  extended  experi- 
mentation are  much  needed  to  fully  explain  the  many  anomalies  of  belt  driving. 
There  is  a  repeated  outcropping  in  the  public  prints  of  misapprehension  con- 
cerning these  irregularities,  and  I  hope  that  conclusive  tests  will  be  fully  made 
in  the  near  future. 

JOHN  H.  COOPEE. 

Los  ANGELES,  CAL.,  May,  1883. 


ERRATA.— See  page  310. 


PREFACE 

TO  THE  FIRST  EDITION. 


OOME  of  the  facts  and  figures  given  in  this  treatise  were  originally 
collated  for  private  use,  and  were  printed  in  the  u  Journal  of  the 
Franklin  Institute."  They  are  now  rearranged,  greatly  enlarged,  and  are 
offered  to  the  public  with  the  hope  that  they  may,  at  least,  spare  the 
reader's  time  in  making  searches,  and  help  him  to  extend  his  knowledge 
of  the  subject  treated. 

In  publishing  these  materials,  which  have  been  selected  from  the  best 
available  sources,  foreign  and  American,  my  object  is  to  acquaint  the 
reader  with  existing  written  rules,  together  with  the  particulars  of  work- 
ing examples,  in  order  that  he  may  study  the  subject  for  himself. 

I  fully  believe  that  the  useful  part  of  every  division  of  mechanical  science 
may  be  expressed  in  simple  language,  and  therefore  propose,  in  the  follow- 
ing pages,  to  tell  just  what  all  need  to  know  about  belting,  in  a  way  that 
every  one  will  clearly  understand. 

The  first  five  chapters,  which  make  up  the  greater  part  of  this  treatise, 
may  be  said  to  fitly  represent  the  practice  of  the  workshop  and  factory. 

The  sixth  chapter,  presenting  the  text  and  results  entire  of  Mr.  Briggs's 
elaborate  essay,  with  Mr.  Towue's  reliable  experiments,  forms  in  itself  a 
theoretical  and  practical  record  of  the  tension  of  leather  belts  of  the 
highest  permanent  value. 

I  have  given  in  the  seventh  chapter,  by  the  aid  of  an  efficient  translator, 
a  literal  and,  I  believe^  an  exact  reproduction  of  the  subject-matter  and 
experiments  of  Morin  on  the  variation  of  the  tension  of  leather  belts,  with 
every  figure,  formula,  and  tabular  statement  exactly  as  it  exists  in  the 
original,  repeating,  also,  the  measures  in  metres  and  the  weights  in 
kilogrammes.  As  Morin  is  frequently  quoted  in  detached  portions,  I  felt 
it  to  be  right,  as  it  is  in  keeping  with  the  work  I  had  undertaken,  to  at 
least  attempt  a  full  and  complete  translation  of  his  words  and  meaning 
into  plain  English. 

B  i 


11  PREFACE. 

The  eighth  chapter  is  devoted  to  the  transmission  of  power  by  ropes, 
beginning  with  the  particulars  and  practice  of  wire-rope  driving,  by  the 
Roeblings,  selected  from  printed  matter,  full  of  good  and  standard  data, 
generously  offered  by  them,  embracing  also  an  article  from  the  French  of 
A.  Achard,  which,  like  Morin's,  contains  some  mathematical  nuts  for  the 
curious  to  crack,  besides  the  opened  kernels  of  fact,  all  of  which  may 
prove  both  pleasant  and  profitable  to  find. 

Finally,  in  chapter  ninth,  Mr.  Wicklin's  liberality  has  enabled  me  to  lay 
before  the  reader  a  particular  account,  in  unmistakably  clear  language,  of 
his  method  of  transmitting  power  by  the  friction  of  rolling  contact. 

I  have  endeavored,  in  all  parts  of  this  work,  to  discover  and  name  the 
author  of  every  statement  made ;  and,  in  addition  to  this,  I  offer  my  thanks 
to  Messrs.  Alexander  Bros.,  Philadelphia;  Messrs.  D.  Appleton  &  Co.,  New 
York;  Mr.  II.  C.  Baird,  Philadelphia;  Messrs.  Brown  &  Allen,  New  York; 
.Mr.  R.  H.  Buel,  New  York;  Mr.  James  Christie,  of  Pencoyd  Iron  Works, 
Philadelphia;  Messrs.  Hoyt  Bros.,  New  York;  the  "Journal  of  the  Frank- 
lin Institute,"  Philadelphia;  "The  Polytechnic  Review,"  Philadelphia; 
Profs.  Morton  and  Thurston,  of  the  Stevens  Institute,  Hoboken ;  Mr.  J. 
W.  Nystrom,  Philadelphia ;  Mr.  Samuel  Webber,  N.  H. ;  and  to  many 
others,  whose  names  are  appended  to  their  contributions,  for  favorable 
opinions  kindly  expressed,  and  for  the  privilege,  freely  given,  of  making 
extracts  from  their  published  works. 

JOHN   H.  COOPER. 
135  Wister  Street, 

GERMAN-TOWN,  PHILA., 

May,  1877. 


CONTENTS. 


PAGE 

INTRODUCTION v 

CHAPTER  I. 

RULES  AND  DATA  FOB  BELTING .     17 

CHAPTER  II. 

METHODS  OF  BELT  TRANSMISSION 154 

CHAPTER  III. 

CEMENTS,  ADHESIVES,  AND  FASTENINGS.        ...„„.  181 

CHAPTER  IV. 

VARIETIES  OF  BELTING       .........      190 

CHAPTER  V. 

STRENGTH  OF  BELTING  LEATHER 210 

CHAPTER  VI. 

EXPERIMENTS  OF  BRIGGS  AND  TOWNE  ON  LEATHER  BELTS        .        .      214 

CHAPTER  VII. 

EXPERIMENTS  ON  THE  TENSION  OF  BELTS,  BY  A.  MORIN        «        .        .  232 

CHAPTER  VIII. 

ROPE  TRANSMISSION  OF  POWER 253 

CHAPTER  IX. 

FRICTIONAL  GEARING  .  288 


INTRODUCTION. 


EXPLANATIONS. 

IN  order  to  lessen  labor  I  have  introduced  two  abbreviations ;  — 
-*-  Rpm  for  revolutions  per  minute,  and  Fpm  for  feet  per  minute,  which 
I  have  found  useful  in  the  every-day  pocket-book  jottings  of  business. 


The  Greek  letter  n,  as  in  all  mathematical  formulae,  stands  for 
3.1416,  denoting  the  circumference  of  a  circle  whose  diameter  is  1. 
On  page  49  is  a  formula  in  which  6.28  occurs.  This  is  meant  to  be 
2  n,  or  3.1416  x  2.  The  signification  of  all  other  Greek  letters  is 
given  in  the  articles  where  they  are  used. 


In  Chap.  7  the  comma  ( ,)  is  used  for  the  same  purpose  that  we 
employ  the  period  (.)  ;  that  is,  to  divide  the  decimals  from  the  whole 
numbers ;  and  the  period  is  not  used  at  all  to  denote  any  operation 
to  be  performed  in  the  formulae ;  while  in  Art.  181  the  comma  is  used 
for  the  decimal  point,  and  the  period  for  the  sign  of  multiplication. 
See  formula  at  head  of  page  266,  where  the  numbers  are  separated 
by  both  periods  and  commas. 


Three  .dots,  thus,  (.'.)  stand  for  therefore. 

The  angular  character  «)  means  less  than,  and  the  same  re- 
versed (>)  means  greater  than.  Thus  A<^£  is  the  same  as  saying 
A  is  less  than  B,  and  C^>D  is  the  same  as  saying  C  is  greater  than/). 


The  word  logarithms  is  thus  abbreviated  :  log. 


The  words  "  No.  1  and  following,"  on  page  242,  refer  to  articles 
in  Morin's  memoir  of  experiments  on  the  friction  of  journals. 

v 


VI 


INTRODUCTION. 


The  metre  is  equal  to  39.37043  inches,  or  it  is  equal  to  3.2808693 
feet ;  or,  to  give  the  length  of  a  metre  in  terms  of  English  measure, 
and  in  a  way  easily  remembered,  it  is  quite  near  to  call  it  equal  to 
3  feet  3  inches  and  f  ths  of  an  inch. 

The  metre  is  divided  into  one  thousand  equal  parts,  each  part 
called  a  millimetre.  Therefore,  to  express  a  measure  by  this  system, 
this  form  is  chosen :  3m,425  —  a  distance  equal  to  3  metres  and  425 
millimetres,  or  3  metres  and  425  thousandths  of  a  metre.  The  fol- 
lowing table  gives  all  the  minor  metric  denominations  and  their 
equivalents  in  English  measure. 


METRES. 

INCHES. 

FKET. 

1  millimetre      .... 

1 

0  03937 

1  centimetre  

1  000 

0  39370 

1  decimetre 

100 

1 

3  93704 

1  metre  •  .       •  •    •  « 

1  0 

1 

39  37043 

3  2808693 

The  gramme  is  equal  to  15.43234874  grains,  and  the  kilogramme  is 

1000  grammes,  or  it  is  equal  to  15-482^4A87n4X  10QQ^2.20462125  Ibs., 

1 000 

and  to  express  kilogrammes  and  fractions,  the  following  form  is  used  : 
56k,824  —  meaning  56  kilogrammes,  and  824  thousandths  of  a  kilo- 
gramme, or  56.824  grammes. 


The  unit  of  measure  for  man-power,  established  by  Morin,  is  the 
equivalent  of  50  Ibs.  raised  1  foot  in  a  second  of  time,  and  that  of  a 
horse-power,  established  by  Watt,  is  the  equivalent  of  550  Ibs.  raised 
1  foot  in  a  second,  which  is  deduced  from  the  original  data  given 
herewith : 

"  Mr.  Watt  made  some  experiments  on  the  strong  horses  employed 
by  the  brewers  in  London,  and  found  that  a  horse  of  that  kind, 
walking  at  the  rate  of  2^  miles  per  hour,  could  draw  150  pounds 
avoirdupois,  by  means  of  a  rope  passing  over  a  pulley,  so  as  to  raise  up 
that  weight,  with  vertical  motion,  at  the  rate  of  220  feet  per  minute. 
This  exertion  of  mechanical  power  is  equal  to  33,000  pounds  raised 
vertically  through  a  space  of  one  foot  per  minute,  and  he  denominated 
it  a  horse-power,  to  serve  for  a  measure  of  the  power  exerted  by  his 
steam-engines."— John  Farey  on  the  Steam- Engine,  London,  1827. 


INTRODUCTION. 


Vll 


The  following  equation  will  make  this  clear : 
5280  x  2i  x  150 


60 


=  33,000  Ibs.,  raised  1  foot  in  a  minute.     This 


unit  of  measure  is  employed  in  this  treatise,  and  is  the  form  of  ex- 
pression used  in  this  country,  because  it  is  customary  to  give  the 
speeds  of  machines  in  feet,  or  revolutions  per  minute.  In  Europe,  the 
unit  of  time  for  the  expression  of  speeds  is  the  second,  not  the  minute. 


Units  for  Horse-Power,  from  Nystrom. 


HORSE- 
POWER. 

FOOT-LBS. 

PER 

SECOND. 

English... 

33,000  Ibs.,  raised  1  foot  per  minute  

550 

French.... 
German 

75  kilogrammes,  raised  1  metre  per  second*... 

542.47 

58225 

Swedish... 

54206 

Russian... 

550 

*  Equal  to  0.986  of  an  English  horse-power. 


The  letters  employed  in  the  opening  formulae  of  Morin's  essay 
are  explained  on  pages  235-7,  the  same  being  used  in  the  formulae 
relating  to  the  friction  of  journals,  given  in  his  earlier  articles. 

Morin's  work  is  published  under  the  authority  of  the  Institute  of 
France,  which  in  itself  is  the  highest  recommendation  of  its  intrinsic 
value.  This  is  also  abundantly  proven  by  the  universal  employment 
of  his  deductions  by  subsequent  writers,  and  by  the  invariable  coin- 
cidence of  results  with  those  obtained  from  all  later  experimentation, 
so  that  it  needs  no  introduction  to  the  reader  other  than  to  say  the 
translation  here  given  is  an  exact  reproduction  of  the  original. 


The  author  of  Art.  58  is  the  same  referred  to  in  the  preface,  and  I 
call  attention  to  his  clear  and  fully  detailed  experiments  on  a  double 
leather  belt,  as  well  as  to  the  mention  of  those  of  larger  dimensions 
employed  in  rolling  mills. 


On  page  165  the  word  rigger  is  used,  and  in  this  case  it  is  clearly 
synonymous  with  small  pulley  or  drum.  Rigger,  in  "  Weale's  Dic- 
tionary of  Tierms  of  Art,"  is  defined  "  a  wheel  with  a  flat  or  slightly 
curved  rim,  moved  by  a  leather  band."  Box,  in  his  "  Treatise  on 
Mill  -Work,"  repeatedly  says  "  rigger  or  pulley,"  as  if  they  were  one 


Vlll  INTRODUCTION. 

and  the  same ;  but  I  do  not  find  the  word  in  use  by  Abel,  Baker, 
Buchanan,  Fairbairn,  Rankine,  or  "  The  Engineer  and  Machinist's 
Assistant." 

Buchanan  says,  on  page  xx.  of  his  preface :  "  Arkwright  used  iron 
bevel-wheels  and  band-pulleys  in  the  cotton  spinning  mills  at  Crom- 
ford  and  Belper,  in  1775.*' 

The  term  bays,  used  on  pages  137-8,  may  be  defined  as  the  spaces 
in  a  ceiling  or  roof  of  a  building  marked  by  the  rafters  or  beams,  or 
by  the  buttresses  or  pilasters  of  the  walls. 


The  figures  given  in  Arts.  68  and  96  coincide  exactly  with  those 
in  Art.  163,  which  leads  one  to  believe  they  were  derived  from  Mr. 
To wne's  published  experiments. 

The  reader  will  be  surprised  and  amused  at  the  different  results  to 
which  the  rules  here  assembled  lead  him,  and  he  may  find  it  a  difficult 
task  to  reconcile  them  to  what  in  his  view  may  be  considered  a  fair 
average  performance  of  a  belt ;  but  as  they  are  exhibited  exactly  as 
I  found  them,  no  apology  is  offered  for  their  repetition  word  for 
word,  and  herein,  indeed,  consists  the  true  value  of  this  collection,  in 
which  will  be  found  in  one  volume  a  great  variety  of  data  gathered 
in  from  many.  _ 

I  give  below  what  may  be  termed  the  philosophy  of  the  belt,  in 
which  the  principles  of  action  are  presented,  and  have  added  the 
mechanics  of  belting,  introducing  dimensions  which  may  not  be  re- 
liable in  practice  for  definite  rules,  because  of  the  greatly  varied  cir- 
cumstances under  which  belts  are  used  ;  yet  when  certain  attainable 
conditions  are  fulfilled,  belts  will  transmit  forces  commensurate  with 
the  area  of  pulley  contact.  The  statements  made  on  pages  9-11 
are  founded  upon  experiment,  backed  up  by  good  authority,  and 
may  be  depended  upon  for  general  practice. 

The  Philosophy  of  Belting. 

"Motion  communicated  by  cords,  bands,  or  straps,  is  remarkably  smooth, 
and  free  from  noise  and  vibration,  and  on  this  account,  as  well  as  from  the 
extreme  simplicity  of  the  method,  it  is  always  preferred  to  every  other,  un- 
less the  motion  is  required  to  be  conveyed  in  an  exact  ratio. 

"As  the  communication  of  motion  between  the  wheels  and  bands  is  en- 
tirely maintained  by  the  frictional  adhesion  between  them,  it  may  happen 
that  it  may  occasionally  fail  through  the  band  sliding  on  the  pulley.  This, 
if  not  excessive,  is  an  advantageous  property  of  the  contrivance,  because 
it  enables  the  machinery  to  give  way  when  unusual  obstructions  or  resist- 
ances are  opposed  to  it,  and  so  prevents  breakage  and  accident.  For  ex- 


INTRODUCTION.  IX 

ample,  if  the  pulley  to  which  motion  is  communicated  were  to  be  suddenly 
stopped,  the  driving  pulley,  instead  of  receiving  the  shock  and  transmitting 
it  to  the  whole  of  the  machinery  in  connection  with  it,  would  slip  round 
until  the  friction  of  the  band  upon  the  two  pulleys  had  gradually  destroyed 
its  motion.  But  if  motion  is  to  be  transmitted  in  an  exact  proportion,  for 
example,  such  as  is  required  in  clock  work,  where  the  hour  hand  must  make 
one  exact  revolution  while  the  minute  hand  .revolves  exactly  12  times, 
bands  are  inapplicable ;  for  supposing  it  practicable  to  make  the  pulleys  in 
so  precise  a  manner  that  their  diameters  should  bear  the  exact  proportion 
required,  which  it  is  not,  this  liability  to  slip  would  be  fatal. 

kl  But  in  all  that  large  class  of  machinery  in  which  an  exact  ratio  is  not 
required  to  be  maintained  in  the  communication  of  rotation,  endless  bands 
are  always  employed,  and  are  capable  of  transmitting  great  forces." — Prof. 
Willis's  Mechanism. 

The  Practical  Mechanics  of  Belting. 
Force  Required  to  Break  Belts. 

The  mean  ultimate  strength  of  a  single  belt  one  inch  wide  and  | 
inch  thick,  made  of  good  leather,  may  he  taken  at  1000  Ibs.  in  the 
solid  part ;  and  ordinary  leather  belts  will  average  |  of  this  amount. 
(See  pages  14,  212,  and  213.) 

The  strength  of  fastenings  varies  according  to  the  loss  of  section 
by  the  rivet  and  lace  holes,  and  by  the  tenacity  of  the  cements  and 
lace  leather  used.  The  weakening  effect  of  the  several  methods  of 
joining  the  ends  of  belts  is  such  that  no  more  than  200  Ibs.  per  inch 
of  width  can  be  depended  upon  for  ultimate  strain.  (See  Art.  163.) 

We  do  not  have  a  sufficient  number  of  tests  of  other  belting 
materials  to  compare  fairly  with  leather,  and  can  therefore  only 
refer  the  reader  to  the  figures  on  page  213. 

Force  Transmitted  by  Belts. 

Each  inch  of  width  of  good  leather  belting  will  transmit  a  force  of 
55  Ibs.,  and  this  may  be  depended  upon  for  continuous  service  when 
the  belt  is  properly  surfaced  on  smooth  pulleys  running  at  high 
speeds.  (See  Arts.  1,  15,  and  40.) 

Taking  the  average  thickness  of  belts  at  J  of  an  inch,  this  would 
give  a  strain  to  the  square  inch  of  section  equal  to  330  Ibs.  (See 
Art.  1.) 

A  strain  of  55  Ibs.  to  the  inch  of  width  is  equal  to  a  surface 
velocity  of  50  square  feet  per  minute  per  horse-power,  which  is  safe 
practice  for  single  belts  in  good  condition  ;  and  on  double  belts  a 
strain  proportioned  to  the  thickness  may  be  used ;  in  all  cases  there 
must  be  ample  contact  with  the  pulleys.  (See  Arts.  1, 15,  and  103.) 

To  facilitate  the  conversion  of  belt  strains  into  surface  velocity,  the 
following  table  is  given  : 


INTRODUCTION. 


Table  for  Converting  the  Strain  upon  a  Belt  into  its  Surface  Velocity 
per  Horse-Power,  and  Vice  Versa. 

These  figures  were  obtained  by  dividing  33,000  by  12  times  the 
strain  in  Ibs.,  to  which  one  inch  of  width  of  belt  may  be  subjected. 

Example. 


10  X 


LBS.  OF  STRAIN 
ON  EACH  INCH  OF 
WIDTH  OF  BELT. 

SQUARE  FEET 
OF  BELT 
PER  MIN. 

PER 

HORSE-POWER. 

LBS.  OF  STRAIN 
ON  EACH  INCH  OF 
WIDTH  OF  BELT. 

SQUARE  FEET 
OF  BELT 
PER  MIN. 

PER 
HORSE-POWER. 

LBS.  OF  STRAIN 
ON  EACH  INCH  OF 
WIDTH  OF  BELT. 

«    g 

W  H  £   £ 

fa  hj  «  5 

s|!i! 

£o«  3 
£    & 

10 

275. 

41 

67.0731 

71 

38.7323 

11 

250. 

42 

65.4761 

72 

38.1944 

12 

229.1666 

43 

63.9534 

73 

37.6712 

13 

211.5384 

44 

62.5 

74 

37.1621 

14 

196.4285 

45 

61.1111 

75 

36.5853 

15 

183.3333 

46 

59.7826 

76 

36.105 

16 

171.875 

47 

58.5106 

77 

35.6371 

17 

161.7647 

48 

57.2916 

78 

35.1812 

18 

152.7777 

49 

56.1224 

79 

34.7368 

19 

144.7368 

50 

55. 

80 

34.375 

20 

137.5 

51 

53.9215 

81 

33.9506 

21 

130.9523 

52 

52.8846 

82 

33.5365 

22 

125. 

53 

51.8867 

83 

33.1325 

23 

119.5652 

54 

50.9259 

84 

32.738 

24 

114.5833 

55 

50. 

85 

32.3529 

25 

110. 

56 

49.1071 

86 

31.9767 

26 

105.7692 

57 

48.2456 

87 

31.6091 

27 

101.8518 

58 

47.4137 

88 

31.25 

28 

98.2142 

59 

46.6101 

89 

30.8988 

29 

94.8275 

60 

45.8333 

90 

30.5555 

30 

91.6666 

61 

45.0819 

91 

30.2197 

31 

88.7096 

62 

44.3548 

92 

29.8913 

32 

85.9375 

63 

43.6507 

93 

29.5698 

33 

83.3333 

64 

42.9687 

94 

29.2553 

34 

80.8823 

65 

42.3076 

95 

28.9473 

35 

78.5714 

66 

41.6666 

96 

28.6458 

36 

76.3888 

67 

41.0447 

97 

28.3505 

37 

74.3243 

68 

40.4411 

98 

28.0612 

38 

72.3684 

69 

39.855 

99 

27.7777 

39 

70.5128 

70 

39.2857 

100 

27.5 

40 

68.75 

1 

INTRODUCTION.  XI 

Conditions  to  be  Fulfilled  in  the  Use  of  Belts. 

Special  conditions  of  successful  practice,  within  which  is  embraced 
the  driving  capacity  measurable  by  the  area  of  contact,  and  modified 
by  the  state  of  the  pulley  and  belt  surfaces,  and  adhesive  used,  which 
must  not  permit  the  belt  to  slip  or  stick ;  the  proper  material  for, 
and  treatment  of  belts ;  the  utmost  contact  or  arc  of  enrolment  on 
the  pulley ;  the  proportion  of  diameter  of  pulley,  and  length  and 
width  of  belt  for  best  running  ;  the  least  rounding  of  the  pulley  faces, 
and  the  greatest  smoothness  obtainable ;  the  hair  side  of  leather  belts 
always  to  pulleys,  as  it  is  the  smoother  side,  for  what  is  lost  in  contact 
must  be  made  up  in  strain,  and  because  the  stronger  fibres  lie  nearest 
the  flesh  side,  and  should  be  preserved ;  the  amount  of  adhesion  or 
traction  developed  by  the  tension  employed ;  the  fastenings,  which 
should  be  of  the  best ;  the  disposition  of  the  laps  such,  that  the  motion 
of  driving  will  run  with,  not  against,  them  ;  the  employment  of  large 
pulleys,  high  speeds,  and  light  belts ;  the  careful  putting  on  and  skil- 
ful joining  of  belts ;  the  running  of  them,  slack  as  possible,  in  the 
upper  fold  or  strip ;  the  avoidance  of  tightness  by  excessive  strain 
or  binders,  and  of  lateral  straining,  as  in  some  quarter  twist  methods ; 
the  introduction  of  fly-wheels,  or  like  devices,  for  rendering  the  work 
of  the  belt  uniform  ;  the  increase  of  driving  capacity,  for  overcoming 
occasional  resistances  and  starting  frictions ;  the  uniformity  of  belt 
section,  and  weight  and  texture  of  material,  the  straightness  of  edges 
for  smoother  running  at  high  speeds ;  the  employment  of  gum  belts 
for  elevators,  or  to.  run  in  moist  or  hot  situations,  or  where  uniformity 
of  section,  without  joints,  is  desirable  —  in  fact,  in  many  places  where 
leather  is  generally  used,  always  avoiding  twists,  all  devices  rubbing 
the  edges,  and  the  contact  with  any  solvent  of  gum  ;  the  adoption  of 
leather  covering  for  pulleys,  by  which  33  per  cent,  of  adhesion  is 
gained ;  the  securing  of  strips  to  the  outer  edges  of  single  belts  to 
increase  adhesion ;  the  running  of  a  belt  atop  of  another  to  make  it 
drive ;  increasing  the  speed  of  a  belt,  which  may  be  as  high  as  a 
mile  in  a  minute  and  be  safe  and  advantageous.  The  introduction 
of  the  devices  for  augmenting  the  tractive  pull  of  belts ;  the  utiliza- 
tion of  belts  for  imparting  and  arresting  motion  ;  the  substitution  of 
"  wrapping  connectors  "  for  gear,  as  in  twist  belt  arrangements,  which 
do  not  over-strain  the  fibres ;  these,  and  a  multitude  of  other,  con- 
ditions, involving  the  essential  elements  of  best  practice,  will  be 
found  on  examination  to  be  accepted  and  used  by  the  numerous  au- 
thorities quoted,  and  to  which  the  reader  is  directed  and  assisted  by 
a  complete  index,  arranged  especially  for  ready  reference. 


Xll  INTRODUCTION. 

Vulcanized  Rubber  Belts,  by  the  N.  Y.  Belting  and  Packing  Co. 

In  Art.  148,  I  have  given  in  detail  many  facts  relating  to  the  helting 
fabricated  by  this  company ;  but  since  that  was  written,  belts  of  larger 
proportions,  and  of  more  perfect  workmanship,  if  such  be  possible,  have 
been  produced.  As  an  evidence  of  the  extent  to  which  their  belting  is 
employed,  "they  manufactured  in  the  year  1875  over  1,200,000  feet  of 
various  widths  of  belting,  and  some  idea  may  be  formed  of  the  magnitude 
of  their  industrial  operations  when  we  mention  one  order  lately  filled 
amounting  to  $45,000,  which  included  many  large  and  long  belts,  and  also 
one  driving  belt  for  the  elevator  of  the  New  York  Central  and  Hudson 
River  Railroad,  which  measured  48  inches  in  width,  330  feet  in  length,  and 
weighed  4000  pounds,"  thus  outdoing  their  "Champion  Belt,"  described 
on  page  197,  and  producing  a  belt  larger  than  "  the  largest  belt  in  the  world," 
of  which  account  is  given  in  Art.  76. 

In  order  to  fairly  present  the  scientific  improvements  developed  by  this 
Company,  and  the  mechanical  perfection  to  which  their  processes  of 
manufacture  have  been  brought,  I  beg  leave  to  offer  in  part  the  report  of 
L.  C.  de  Montanville  and  E.  Sternhein,  agents  of  the  French  Government 
to  the  Centennial,  not  omitting  the  grand  compliment  they  have  paid  us 
in  the  following  words,  which  should  be  written  in  letters  of  gold  : 

"The  Philadelphia  exhibition  was  the  greatest  manifestation  of  indus- 
trial work,  in  all  its  ramifications,  ever  offered  to  mankind,"  and  then 
proceed  to  requote  the  "praiseworthy  terms  in  which  Messrs.  Kuhlmann, 
Jr.,  and  Dietz-Monin,  of  France,  and  Mr.  De  Wilde,  of  Belgium,  spoke  of 
the  manufactured  products  exhibited  by  this  establishment."  They  said : 

"  For  some  years  past  India-rubber,  which  has  passed  through  so  many  new  pro- 
cesses, has  formed  the  basis  of  several  large  industries,  which  inanufacture  an  infinite 
variety  of  articles  useful  in  domestic  economy,  as  well  as  various  instruments  of 
undoubted  value,  not  only  to  surgery,  but  also  to  the  physical,  chemical,  and  me- 
chanical arts,  and  to  navigation.  Up  to  the  present  time,  we  have  observed  no 
more  important  progress  in  this  manufacture  than  that  of  the  introduction  of  Oxide 
of  Lead,  Zinc,  and  Sulphur  in  the  vulcanization  of  rubber,  thus  rendering  it  capable 
of  being  used  for  mechanical  purposes.  What  we  especially  noticed  in  the  goods 
manufactured  by  the  Company  which  is  the  present  subject  of  our  special  attention, 
was  that  their  rubber  fabrics  retained  their  flexibility,  and  all  their  essential  quali- 
ties, without  the  slightest  alteration,  even  when  subjected  to  the  most  opposite 
temperatures.  We  cannot  too  highly  praise  its  special  excellencies — namely,  its  re- 
sistance to  the  action  of  chemical  agents,  the  perfect  smoothness  of  its  surface,  and 
the  evenness  of  its  vulcanization.  The  tests  that  we  made  of  the  different  bands 
manufactured  by  this  Company,  and  destined  for  use  as  machine  belting,  showed  us 
conclusively  that,  in  addition  to  the  above-mentioned  good  qualities,  it  possessed 
great  tenacity  and  large  power  of  resistance  iinder  great  pressure.  For  these  im- 
portant reasons,  we  should  prefer  its  use  for  driving  machinery  even  to  the  best  and 
thickest  leather  belting.  The  mixture  of  Oxide  of  Lead,  Zinc,  and  Sulphur  used  in 
combination  with  the  rubber  during  its  process  of  vulcanization,  obviates  all 
tendency  to  its  becoming  hardened  or  rigid  by  extreme  cold,  or  to  its  softening  and 
becoming  porous  under  the  influence  of  heat.  These  probabilities,  which  were 
serious  obstacles  to  the  general  use  of  vulcanized  rubber  for  such  purposes,  are,  in 
our  opinion,  completely  overcome  by  the  use  of  Oxide  of  Lead,  Zinc,  and  Sulphur. 
We  cannot  do  better  than  follow  these  remarks  by  giving  verbatim,  and  without 
further  comment,  the  very  flattering  terms  in  which  the  jury  of  Philadelphia 
spoke  of  the  New  York  Belting  and  Packing  Company.  Their  official  report  reads 
as  follows : 


UNCLASSIFIED    FIGURES     AND    NOTES.  Xlll 

PHILADELPHIA,  December  20th,  1876. 

REPORT  ON  AWARDS. 

Product,  Rubber  Belting. 

Name  and  address  of  Exhibitor,  New  York  Belting  and  Packing  Company,  New 
York  City. 

The  undersigned,  having  examined  the  product  herein  described,  respectfully 
recommends  the  same  to  the  United  States  Centennial  Commission  for  Award,  for 
the  following  reasons,  Viz. : 

The  belting  is  of  various  widths  to  48  inches,  of  thickness  from  three  to  five  ply, 
of  length  to  320  feet.  Its  strength,  as  determined  by  experiment  under  direction  of 
Capt.  Albert:  A  three-ply  three  inch  belt  gave  way  at  3,000  (three  thousand) 
pounds.  In  adhesion,  a  six  inch  belt,  with  a  weight  of  fifty  pounds  at  either  end, 
over  a  15|  inches  exterior  diameter  smooth,  cast-iron  fixed  pulley,  slipped  at  70 
(seventy)  pounds.  The  thickness  of  the  belt  was  three-ply — ^  of  an  inch.  Com- 
mended for  adhesion,  strength,  smooth  finish,  and  care  in  workmanship  and  curing. 

E.  N.  HOKSFORD. 

UNCLASSIFIED  FIGURES  AND  NOTES. 
From  "Tables,  Rules,  and  Data,  by  D.  K.  Clark,"  London,  1877. 

Average  Tension. 

"  Dr.  Hartig  found,  from  the  results  of  experiments  made  by  him 
in  a  woollen  mill,  that  the  tension  of  the  driving  belts  varied  from 
30  Ibs.  to  532  Ibs.  per  square  inch  of  section,  and  that  it  averaged 
273  Ibs.  per  square  inch." 

Average  Working  Strain. 

"  An  average  working  strength  of  300  Ibs.  per  square  inch  of 
section  of  leather  belts  may  be  accepted  for  purposes  of  calculation." 

Surface  Velocity. 

"  The  performances  of  belts  may  be  compared  by  calculating  the 
number  of  square  feet  of  belt-surface  passed  over  either  pulley  per 
minute  per  horse-power;  involving  the  elements  of  working  stress 
and  velocity.  It  is  found  by  multiplying  the  velocity  in  feet  per 
minute  by  the  breadth  of  the  belt  in  feet,  and  dividing  the  product 
by  the  horse-power  transmitted." 

Rule  for  Horse- Power  of  a  Belt. 

"  M.  Claudel  gives  the  following  empirical  formula,  in  common 
use,  for  finding  the  breadth  of  a  leather  belt  enveloping  half  the 
circumference  of  a  pulley. 

TT 

Altering  the  measures :         b  =  c  —  : 

In  which  b  =  breadth  of  belt  in  inches. 
H  —  horse-power. 

v  =  the  speed  of  the  belt  in  feet  per  second, 
c  —  a  constant  =  26  for  upright  shafts  and 
20  for  horizontal  shafts. 


XIV 


UNCLASSIFIED    FIGURES    AND    NOTES. 


"M.  Claudel  instances  the  common  experience  that  a  belt  3| 
inches  broad,  moving  at  a  velocity  of  9  feet  per  second,  can  very 
well  transmit  one  horse-power  with  ordinary  tension,  and  without 
over-straining,  working  on  turned  and  smooth  pulleys  of  equal 
diameter. 

"  This  example,  if  adopted  as  a  basis,  would  give  a  coefficient 
e  =  29.  The  working  tension  is  only  about  20  Ibs.  per  inch  wide. 
At  the  same  time,  the  values  given  by  the  empirical  formula  are 
little  more  than  those  deducible  from  the  data  of  M.  Morin." 


Kirkaldy's  Tests  of  Norris  &.  Co.'s  Belting,  gave  the  following 
Results  for  Ultimate  Tensile  Strength. 


SIZE. 

ENGLISH 
BELTING. 

HELVETIA 
BELTING. 

ENGLISH 
PER  INCH  . 
OF  WIDTH. 

HELVETIA 
PER  INCH 
OF   WIDTH. 

12  inch  double  .. 

14  861  Ibs 

17  622  Ibs 

1238 

1469 

7      «<          «« 

6  193    " 

11  089  " 

884 

1584 

6     "        " 

5  603   " 

10  456  " 

934 

1743 

4     «        "        

4365    " 

6207  " 

1091 

1552 

2    "        "      

2942    " 

4237  " 

1471 

2118 

10     "       single  

8  846    " 

11  888  " 

885 

1189 

5     "        "       

4060   " 

5426  " 

812 

1085 

4.    «        « 

3  248    " 

3948  " 

812 

987 

34  "        " 

3  007   " 

3  377  " 

859 

965 

°3 

Tightening  Pulleys. 

The  tightening  pulley  is  applied  to  belts  for  increasing  their  adhe- 
sion to  the  pulleys ;  and  as  this  is  liable  to  fail  first  on  the  smaller 
pulley,  it  is  usual  to  place  them  on  the  slack  side  of  the  belt,  nearer 
this  pulley,  in  order  to  increase  adhesion  as  well  as  the  area  of  con- 
tact, which  it  effectually  does  in  this  position ;  but  it  also  increases 
the  friction  of  driving,  in  proportion  to  the  thrusting  of  the  same 
from  the  line  of  its  natural  curvature.  If  placed  nearest  the  larger 
pulley,  it  would  increase  the  adhesion  where  such  is  not  wanted,  and 
would,  at  the  same  time,  diminish  the  area  of  contact  on  the  smaller 
pulley  by  pulling  the  belt  away  from  it,  thus  lessening  the  very  effect 
which  it  was  applied  to  remedy.  It  would,  however,  increase  adhe- 
sion by  augmenting  the  tension  of  the  belt ;  but  this  in  turn  would 
add  to  the  resistance  to  be  overcome,  by  creating  additional  friction 
in  the  shaft  bearings. 


UNCLASSIFIED    FIGURES    AND    NOTES.  XV 

Effect  of  Speed  on  Slack  Belts. 

In  making  close  calculations  for  belt  adhesion,  care  must  be  taken 
to  note  the  degrees  of  contact  of  the  belt  on  the  pulley,  as  the  adhe- 
sion increases  in  a  greater  ratio  than  the  area  of  contact  (Art.  97), 
especially  when  the  upper  fold  is  very  slack  and  the  speed  high, 
in  which  case  the  belt  throws  itself  against  the  face  of  the  pulley  it 
is  approaching  with  much  force,  increasing  the  area  of  contact,  as 
well  as  the  pressure  on  the  pulley. 

This  banking  of  the  current  of  the  belt  against  the  face  of  the 
pulley  augments  adhesion,  and  in  a  great  measure  compensates  for 
the  loss  of  contact  due  to  centrifugal  force. 


Belting  of  Intestines. 

"  Belting  is  made  in  America  from  the  entrails  of  sheep,  which 
average  (the  entrails  —  not  the  sheep)  some  fifty -five  feet  in  length. 
They  are  thoroughly  cleaned,  and  subjected  for  some  days -to  the 
action  of  brine,  and  are  then  wound  upon  bobbins,  after  which  the 
process  is  the  same  as  making  common  rope.  If  a  flat  belt  is  re- 
quired, a  loom  is  employed,  and  the  strands  are  woven  together.  A 
J-inch  rope  thus  made  will  stand  a  strain  of  seven  tons,  and  is  guar- 
anteed to  last  ten  years ;  the  best  hemp  rope  of  same  thickness  has  &, 
life  of  about  three  years." 

To  Measure  for  Belting. 

To  find  the  length  and  course  of  a  belt,  apply  a  tape-line  or  string 
to  the  pulleys  where  the  belt  goes,  and  then  measure  the  length  of 
the  string  by  a  two-feet  rule,  which  a  mechanic  should  always  have 
at  hand  ;  and  when  such  measure  cannot  be  made,  make  a  drawing, 
full  size  or  to  scale,  and  step  dividers  around  the  course  of  the  belt. 
By  means  of  such  drawings,  the  places  where  the  belt  passes  floors 
and  the  like  can  also  be  found.  These  methods  are  more  trusty  and 
more  convenient  than  any  system  of  calculations,  however  tabulated, 
formulated,  or  prepared. 

Pulleys  of  Paper  and  Raw-Hide. 

Pulleys  may  be  made  of  paper  and  of  raw-hide  in  the  same  man- 
ner as  directed  in  Art.  61  for  leather  pulleys.  Raw-hide  has  superior 
qualities  for  resisting  wear;  it  may  therefore  be  very  successfully 
used  for  shaft  bearings  or  for  the  hubs  of  loose  pulleys. 

Paper  also  suits  well  for  pulley  covers. 


A  TREATISE 


ON  THE 


USE  OF  BELTING 


CHAPTER  I. 

RULES  FOR  ASCERTAINING  THE  DRIVING  POWER  OP  BELTS, 
AND  FACTS  AND  FIGURES  RELATING  THERETO. 

Mr.  Samuel  Webber,  C.  E.,  of  Manchester,  N.  H.,  who  has  much 
practical  acquaintance  with  mill  work  and  belting,  says : 

1.  "  I  have  had  a  working  rule  for  many  years,  which  was  given  to 
me  by  an  old  and  experienced  machinist,  and  may  be  thus  expressed  : 
Ordinary  leather  belting  one  inch  wide,  having  a  velocity  of  600  Fpm, 
will  transmit  one  horse-power. 

"  Practice  has  shown  me  the  safety  of  this  rule,  and  for  which,  and 
for  its  extension  to  all  cases,  I  have  sought  a  reason  and  a  formula. 

"After  an  examination  of  the  text-books,  I  found  that  Morin's 
data  gave  me  the  clue  to  the  truth  of  this  rule,  and  that  it  was  sup- 
ported by  other  good  authority.  Morin*says :  '  Belts  designed  for  con- 
tinuous service  may  be  made  to  bear  a  tension  of  0.551  Ibs.  per 
.0000107  square  feet,  or  .00155  square  inches  of  section,  which  en- 
ables us  to  determine  their  breadth  according  to  the  thickness/  This 
is  equal  to  355  Ibs.  per  square  inch  of  belting  leather,  and  is  also 
equal  to  from  |  to  TJ3  the  breaking  strength  of  the  same,  as  given  by 
Rankine  and  other  authorities. 

"  From  this  I  see  my  way  to  a  simple  formula :  Substituting  330 
Ibs.  for  355  Ibs.  per  square  inch,  I  strike  the  component  part  of  a 
horse-power,  and  deduce  the  following :  one  square  inch  of  beking,  at 
a  velocity  of  100  Fpm,  will  transmit  one  horse-power  with  safety,  and 
from  these  data  get  this  rule : 

2  17 


18  RULES     FOR    BELTING. 

"  The  denominator  of  the  fraction  expressing  the  thickness  of  the 
belt  in  inches  gives  the  velocity  in  hundreds  of  feet  per  minute  at 
which  each  inch  of  width  will  transmit  one  horse-power,  that  is :  |  = 
6  x  100  ==  600  ft.  :  \  =  3  x  100  =  300  ft,  and  so  on. 

"  Now,  £  inch  being  about  the  ordinary  thickness  of  a  single  belt, 
this  shows  me  why  my  old  '  rule  of  thumb '  proved  right,  and  a  care- 
ful examination  of  many  of  the  large  belts  running  in  our  New  Eng- 
land cotton-mills  within  the  last  year  or  two  confirms  my  opinion  as 
to  the  safety  of  the  rule. 

"  This  gives  a  strain  of  55  Ibs.  per  inch,  and  a  belt  speed  of  50 
square  feet  of  surface  per  minute  per  horse-power,  as  safe,  ordinary 
practice  for  single  belts ;  and  I  find  the  same  velocity,  with  a  strain 
proportioned  to  the  thickness,  works  perfectly  well  with  double  belts. 
This,  however,  is  applicable  where  there  is  a  sufficient  holding  surface 
on  the  smaller  pulley ;  if  the  arc  of  contact  be  small,  a  wider  belt 
will  be  necessary,  and  I  am  not  yet  able  to  formulate  a  rule  for  belt 
contact.  The  nearest  approach  I  have  made  to  it  yet  is  to  allow  10 
to  12  square  inches  of  pulley  surface  in  contact  with  belt  for  each 
horse-power. 

"  It  is  generally  conceded  that  the  friction  of  a  belt  passing  half 
around  a  pulley,  is  equal  to  one-half  the  strain  on  the  belt ;  or  that 
an  inch  belt,  at  600  Fpm,  with  a  strain  of  55  Ibs.,  would  give  a  trac- 
tion of  27.5  Ibs.  and  require  a  pulley  which  would  give  1200  lineal 
feet  per  minute  of  surface  contact,  to  obtain  the  one  horse-power  to 
which  the  belt  would  be  equal. 

"  Morin,  in  his  '  Mechanics/  gives,  as  the  result  of  actual  trials  with 
a  loaded  belt  over  a  wooden  drum,  an  average  friction  of  57  per  cent., 
which  would  be  increased  by  using  a  pulley  covered  with  leather ;  and 
a  polished  iron  pulley,  with  a  smooth,  flexible  belt,  may,  I  think,  be 
depended  on  in  actual  use  for' 50  per  cent. 

"  The  friction  of  a  belt  varies  with  the  arc  of  the  circle  of  the  pulley 
with  which  it  is  in  contact,  and  is  only  half  as  great  on  \  of  a  pulley 
as  on  ^  of  one ;  so  that  double  the  surface  in  square  inches  will  be  re- 
quired to  transmit  the  same  power  in  the  former  case  that  would  be 
needed  in  the  latter. 

"  Carrying  out  these  rules,  it  will  be  easily  seen  that  where  high 
speed  is  to  be  obtained  by  the  use  of  small  pulleys,  a  much  greater 
width  of  belt  is  necessary  to  get  the  frictional  surface  than  is  called 
for  by  the  strength  of  the  leather ;  and  it  will  be  found  that,  for  cir- 
cular saws,  cotton-pickers,  spinning-frames,  etc.,  a  wider  belt  is  needed 
than  is  due  to  the  actual  power  transmitted.  Take,  for  instance,  a 


RULES    FOB    BELTING.  *  19 

spinning-frame  with  a  7-inch  pulley,  900  Rpm,  or  1650  feet  belt 
velocity,  and  requiring  1^  horse-power.  One  inch  of  belt  at  that 
speed  would  transmit  2^  horse-power,  but  the  contact  surface  of  the 
pulley  would  not  be  over  10  inches  in  length,  and,  by  the  above 
rules,  calls  for  a  3-iiich  belt,  which  is  the  standard  size  for  that  pur- 
pose. Looms,  and  other  machines  which  are  constantly  stopped  and 
started,  also  require  wider  belts,  to  stand  the  wear  and  tear  of  '  ship- 
ping,' than  would  be  needed  for  the  power.  Let  me  cite,  as  an  ex- 
ample, an  instance  of  a  main  belt  running  in  this  city  24  inches  wide, 
double,  transmitting  160  horse-power  at  3200  Fpm,  to  a  pulley  4 
feet  10  inches  diameter.  Taking  my  formula  for  double  belts,  it 
would  be : 

,       160x3660 


"  This  belt  has  run  four  years  without  repairs,  and  looks  likely  to 
run  forty  more.  According  to  my  rules  for  the  strength  of  leather,  it 
would  transmit  192  horse-power,  but  to  do  it  the  smaller  pulley 
should  be  5  feet  9.6  inches  diameter  instead  of  4  feet  10  inches. 

"  My  formula  for  single  belts  is : 

w==  HP  x  5500 

velocity  X  contact  in  ft. 
and  for  double  belts : 

HP  x  3660 


velocity  X  contact  in  ft. 

"  The  tendency  with  us  now  is  to  use  large  pulleys,  high  surface 
speeds,  and  light  belts.  In  my  rules  for  double  belts  I  have  assumed 
J  inch  in  thickness  and  82J  Ibs.  strain ;  but  if  the  belt  be,  as  many 
are,  |  inch  thick,  it  would,  of  course,  bear  from  110  to  120  Ibs.,  and 
300  Fpm  would  give  one  horse-power  per  inch. 

"  One  other  point  I  would  also  mention  :  The  better  friction  is  not 
the  only  reason  for  putting  the  *  grain  '  side  of  the  leather  next  the 
pulley ;  it  is  harder,  and  not  so  elastic  and  fibrous  as  the  flesh  side ; 
will  wear  better  on  the  surface  of  the  pulley,  while  it  will  crack  and 
break  if  exposed  to  the  expansion  and  contraction  to  which  the  out- 
side of  the  belt  is  continually  subjected." 


20 


RULES    FOR    BELTING. 


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21 


Fig.  1. 


2.  "The  Operative  Mechanic  and  British  Machinist,"  by  John 
Nicholson,  Esq.,  C.  E.,  American  ed.,  1826,  makes  mention  of 

"  The  fast  and  loose  pulley,  which 
is  represented  in  Fig.  1.  B  is  a 
pulley  firmly  fixed  on  the  axle 
A,  and  C  a  pulley  with  a  bush, 
so  that  it  can  revolve  upon  the 
axle  A  without  communicating 
motion  to  it.  This  contrivance 
is  remarkable  for  its  beautiful 
simplicity,  as  the  axle  A  can 
be  thrown  in  and  out  of  gear 
at  pleasure,  without  the  least 
shock,  by  simply  passing  a 
strap  from  the  one  pulley  to 
the  other." 

The  above  work  also  describes  the  grooved  sliding  clutch  pulley 
and  the  "  tightening  roller,"  or  pulley  for  increasing  the  tension  of  a 
belt  to  the  tightness  required  for  driving. 

From  "  The  Encyclopedia  of  Arts,  Manufactures,  and  Machinery," 
by  Barlow  &.  Babbage,  London,  1848. 

3.  "  In  the  numerous  contrivances  for  the  purpose  of  engag- 
ing  and   disengaging    machinery,  the   particular  object  aimed    at 
has  been  to  communicate  motion  without  a  shock ;    as,  in  conse- 
quence of  the  inertia  of  bodies,  or  their  disposition  to  remain  in 
the  state  in  which  they  are,  the  parts  of  Machinery,  when  acted 
upon  too  suddenly  by  a  moving  power,  are  liable  to  fracture  and 
derangement. 

"  The  inventions  for  this  purpose  may  be  divided  into  two  classes, 
viz. :  when  the  motion  is  communicated  by  bands,  belts,  or  chains, 
and  when  it  is  communicated  by  wheel  work ;  the  former  generally 
possesses  the  advantage  of  bringing  on  the  motion  more  gradually, 
although  the  application  to  large  Machinery  is  attended  with  incon- 
venience." 

Fig.  2  represents  a  contrivance  termed  the  fast  and  loose  pulley, 
which  is  remarkable  for  its  simplicity.  It  is  attended  with  no  shock, 
and  is  considered  the  most  perfect  method  yet  invented  for  the  pur- 
pose where  it  can  be  applied. 

It  consists  simply  of  two  pulleys,  B  and  C,  one  being  fixed  on  the 
axle,  and  the  other  loose,  and  the  belt  or  band  which  conveys  the 


22  RULES    FOR    BELTING. 

motion  may  be  shifted  at  pleasure,  either  upon  one  pulley  or  the 

other;  by  that  means  put- 
ting in  or  out  of  motion  the 
axle  A. 

It  may  be  proper  here  to 
mention  that,  in  order  to  make 
a  belt  run  properly  on  a  pul- 
ley, it  is  necessary  to  have  the 
rim  a  little  rounded  or  swelled 
in  the  middle.  The  belt  al- 
ways inclines  to  that  part  of 
the  pulley  which  is  of  greatest 
diameter. 

"  This  curious  property  is 
of  great  practical  use,  and, 

until  it  was  known,  it  was  found  very  troublesome  to  prevent  belts 

slipping  off  the  pulleys." 

From  "The  Science  of  Modern  Cotton-Spinning,"  by  Evan  Leigh, 
C.  E.,  Manchester,  England,  1875. 

4.  Mr.  Leigh  advises  us  to  "seize  upon  truth  where'er  't  is  found," 
and  we  therefore  transfer  a  few  of  the  fine  specimens  he  has  given  us 
in  his  excellent  work  on  "  Cotton-Spinning/' 

"  Simplicity,  which  in  all  mechanism  is  desirable,  is  more  especially 
so  in  mill  gearing.  Heavy,  cumbrous,  and  rumbling  gearing  should 
be  avoided  as  much  as  possible.  It  is  always  disagreeable  and  dan- 
gerous, because  the  breaking  of  a  cog,  from  any  hard  substance  get- 
ting in  the  wheels,  often  causes  a  fearful  crash.  The  constant  greasing 
required  is  also  expensive,  and  produces  much  filth  and  unpleasant 
smell." 

"  Looking  around,  one  must  accord  to  America  the  honor  of  many 
useful  inventions.  Give  a  man  a  certain  thing  to  do  with  limited 
means,  and  his  ingenuity  suggests  a  way  of  doing  it ;  so  in  America 
heavy  gearing  is  almost  entirely  discarded,  and  broad  belts  or  straps 
substituted. 

"  Much  may  be  said  pro  and  con  on  this  subject.  The  wisdom  or 
folly  thereof  depends  upon  the  mode  of  application. 

"When  properly  applied,  there  is  no  question  that  the  noiseless 
and  practical  way  in  which  belts  do  their  work  is  preferable  to  gear- 
ing. 

"  If  belting  be  improperly  applied  it  makes  all  the  difference.     A 


RULES    FOR    BELTING.  23 

main  driving-belt,  to  be  rightly  applied,  should  go  through  3000  or 
4000  feet  of  space  per  minute,  and  be  sufficiently  wide  to  drive  all 
the  machinery  and  shafting  it  has  to  turn  quite  easily,  when  running 
in  a  slack  state.  A  wide  belt  moving  with  that  velocity,  on  drums 
of  large  diameter,  possesses  enormous  power.  After  a  new  belt  has 
been  tightened  up  once,  it  should  work  many  years  without  again 
requiring  tightening,  and  will  do  so  if  properly  applied  and  made  of 
good  material,  saving,  in  the  meantime,  all  the  grease  and  labor  of 
putting  it  on  which  gearing  requires,  to  say  nothing  of  the  horrid 
noise  which  heavy  gearing  makes.  In  America  the  main  driving- 
belts  are  open  straps,  worked  in  this  manner  and  neatly  boxed  up,  so 
that  nothing  is  seen,  nothing  heard ;  whilst  in  this  country  the  disa- 
greeable rumbling  noise  of  the  heavy  gearing  of  some  mills  can  be 
heard,  in  country  places,  a  mile  off." 

Ask  "  John  Bull "  whether  he  would  prefer  driving  his  machinery 
by  gearing  or  belting,  and  he  will  shake  his  head  and  tell  you  he 
never  minds  the  noise ;  he  likes  to  be  sure.  "  John  Bull "  is  gener- 
ally a  shrewd  fellow,  but,  as  a  rule,  he  does  not  at  present  understand 
what  a  belt  is  capable  of  when  it  runs  through  3000  or  4000  feet  of 
space  per  minute. 

"  Driving  by  belt  or  band  has  ultimately  to  be  resorted  to  in  all 
cotton-spinning  machinery ;  therefore  the  question  of  certainty  goes 
for  nothing  when  properly  done,  as  one  way  is  just  as  certain  as  the 
other.  To  apply  belting  to  slow-running  shafts  would  be  simply 
ridiculous.  As  speed  has  finally  to  be  attained,  it  should  be 
gained,  as  much  as  possible,  at  once  from  the  periphery  of  the  fly- 
wheel of  quick-running  engines.  The  speed  of  engines  and  diam- 
eter of  fly-wheel  should  be  so  adapted  to  each  other  that  the  rim 
of  the  latter  will  give  off  a  speed  of  3000  to  4000  Fpm  at  least ; 
it  being  borne  in  mind  that  the  power  of  a  belt  is  exactly  as  the 
speed  or  space  it  runs  through  per  minute.  For  example,  a  belt  or 
strap  of  6  inches  wide,  running  through  4000  feet  of  space  per 
minute,  will  turn  as  much  machinery  or  give  off  as  much  power 
as  a  belt  of  24  inches  will  do  that  moves  only  at  the  rate  of  1000 
Fpm.  Therefore  the  quicker  the  speed  the  less  is  the  expense  of 
the  belt. 

"  What  has  been  said  about  slack  straps  applies  to  all  heavy  run- 
ning machinery  throughout.  It  will  be  found  also  a  great  saving  of 
power  to  have  larger  pulleys  than  is  usual  both  on  the  shafting  and 
frames,  so  that  the  straps  can  do  their  work  easily.  This  saves  wear 
and  tear  also  to  a  great  extent.  When  a  strap  is  obliged  to  be  tight 


24  RULES    FOR    BELTING. 

in  order  to  do  its  work,  it  pulls  down  at  the  shafting  and  up  at  the 
pedestals  of  the  frame  it  is  driving,  thereby  wearing  out  the  steps, 
consuming  more  oil,  and  absorbing  power,  besides  pulling  itself  to 
pieces,  in  addition  to  which  it  slips  and  loses  time. 

"  After  a  mill  is  settled  to  work  there  ought  to  be  scarcely  any 
piecing  or  tightening  of  straps,  and  if  the  precautions  above  enu- 
merated be  taken  at  the  commencement,  production  will  go  on  with 
greater  regularity,  and  a  very  large  saving  in  the  aggregate  will  be 
effected. 

"  As  an  example  of  what  may  be  done  with  belts,  the  first  which 
the  author  saw  in  an  American  factory  was  one  driving  140  horse- 
power from  a  drum  of  9  feet  diameter,  and  going  at  the  speed  of 
130  Kpm,  and  driving  a  shaft  which  had  a  drum  of  7  feet  diam- 
eter upon  it.  The  strap  was  24  inches  wide,  of  double  leather 
sewn  together.  It  was  asserted  that  this  strap  had  run  for  seven 
years  without  piecing  or  tightening,  having  been  tightened  only 
once  since  it  was  newly  put  on.  Being  surprised  at  this  statement, 
further  inquiry  was  made  in  different  mills,  which  fully  confirmed 
what  had  been  said  as  to  the  durability  and  ease  with  which  these 
large  belts  do  their  work.  If  reflected  upon,  what  an  impressive 
lesson  this  teaches ! 

"  How  delightful  it  would  be  in  a  mill  if  all  the  straps  would  run 
so  long  without  piecing  or  giving  trouble !  Yet  so  it  would  be  were 
the  same  conditions  observed.  How  much  we  vary  from  those  condi- 
tions will  be  seen  upon  examination.  For  instance,  we  often  see 
carding-engines  with  pulleys  on  the  main  cylinders  12  inches  diame- 
ter, running  at  a  speed  of  140  Rpm,  which  is  equal  to  barely  440 
Fpm  of  space  through  which  the  strap  moves,  whilst  the  big  driving- 
strap,  above  alluded  to,  goes  more  than  eight  times  faster,  being  at 
the  rate  of  over  3673  Fpm.  The  straps  which  drive  frames  and 
other  machinery  are  not  much  quicker  than  those  which  drive  the 
cards. 

"  Therefore  the  lesson  taught  by  the  big  belt  is  imperative,  namely, 
that  there  should  be  very  light  shafting  run  at  a  very  quick  speed, 
with  larger  drums  and  pulleys ;  then  very  little  would  be  heard  of 
strap  piecing,  or  wear  and  tear  of  belts,  working  with  less  power 
and  steadier  production  all  the  while.  'Our  American  cousins' 
have  taught  some  good  things,  and  this  is  one  of  them. 

"  In  new  countries  men  have  new  ways,  and  do  not  fix  their  prin- 
ciples by  inheritance,  as  they  do  in  old  countries. 

"  In  some  American  factories,  one  long  belt  is  made  to  run  the 


RULES    FOR    BELTING. 


25 


whole  round,  from  bottom  to  top  of  mill,  turning  every  main  shaft, 
passing,  where  necessary,  over  carrier-pulleys,  and  working  its  way 
to  and  fro.  This  is  not  a  good  plan,  as  the  belt  is  required  to  be  of 
enormous  length,  and,  having  all  the  stress  upon  it,  is  required  to  be 
sufficiently  wide  to  take  off  all  the  power.  It  is  likewise  more  costly 
than  necessary,  besides  having  other  disadvantages.  The  simplest 


Fig.  3. 

and  best  method  of  driving  by  belt,  also  the  cheapest  and  most 
durable,  is  to  convey  the  power  from  the  main  driving  shaft  direct 
to  each  room  by  a  separate  strap ;  and  if  more  than  one  shaft  is 
wanted  in  any  one  of  the  rooms,  to  drive  it  from  the  other  direct  by 
a  separate  strap,  apportioning  the  width  of  each  strap  to  the  power 
it  is  required  to  drive,  and  where  a  belt  is  necessarily  short,  allowing 
a  little  extra  width. 

"  The  example  below  shows  the  best  method  of  driving  a  mill  of 
four  stories,  in  which  two  shafts  are  required  in  the  bottom  room, 
which  may  be  driven  direct  from  the  first  strap,  as  will  be  seen  in 
Fig.  3,  in  which  a  represents  the  main  driving  shaft,  running  80 


26  RULES    FOB    BELTING. 

Kpm,  driven  direct  from  the  steam-engine  or  other  motor;  b  is  a 
strong,  well  balanced  drum,  of  15  feet  diameter,  and  about  3  feet 
wide,  keyed  on  the  shaft  a,  which,  in  making  80  Rpm,  gives  off  a 
speed  on  its  periphery  of  3768  Fpm  ;  b  1,  b  2,  b  3,  b  4,  b  5,  are  strong 
pulleys  about  6  feet  in  diameter,  and  6  inches  wide,  keyed  on  the 
respective  shafts  they  have  to  drive,  which  will  in  this  case  make  200 
Rpm,  but  may,  of  course,  be  varied  to  run  faster  or  slower  by  putting 
on  smaller  or  larger  pulleys ;  but  whatever  else  is  done,  the  speed  of 
the  straps  must  be  kept  up,  for  in  that  lies  the  whole  secret  of  success 
in  belt  driving. 

"  The  shaft  a,  if  the  power  be  steam,  will  be  the  crank  shaft,  and 
the  drum  upon  it  will  act  as  fly-wheel,  and  have  great  centrifugal 
force,  without  being  heavy,  by  reason  of  its  speed.  The  pulley  must 
be  turned  a  little  convex  at  the  top,  where  every  strap  comes  upon 
it,  having  a  little  flat  space  of  3  or  4  inches  between  every  hump,  to 
admit  of  boxing  up  each  belt  separately,  and  insuring  them  running 
in  their  proper  places. 

"  Should  any  belt  break,  as  it  runs  in  a  separate  box  all  the  way 
up,  it  cannot  in  any  way  interfere  with  the  others.  When  a  belt 
wants  piecing  or  tightening  (a  very  rare  occurrence)  the  ends  are 
fixed  in  cramps,  which  are  drawn  together  by  screws. 

"  As  the  straps  or  belts  in  the  above  example  are  supposed  to  be  6 
inches  wide,  each  belt  is  capable  of  driving  horse-power,  as  the  fol- 
lowing rule  for  calculating  the  power  of  belts  will  show. 

Rule  to  find  the   Horse-power  that  any  given  Width  of  Double 
Belt  is  easily  Capable  of  Driving. 

"  Multiply  the  number  of  square  inches  covered  by  the  belt  on  the 
driven  pulley  by  one-half  the  speed  in  feet  per  minute  through  which 
the  belt  moves,  eand  divide  the  product  by  33,000,  the  quotient  will 
be  the  horse-power. 

Rule  to  find  the  Proper  Width  of  Belt  for  any  given  Horse-power. 

"  Multiply  33,000  by  the  horse-power  required,  and  divide  the  pro- 
duct first  by  the  length  in  inches  covered  by  the  belt  on  the  driven 
pulley,  and  again  by  half  the  speed  of  the  belt. 

"  If  these  rules,  which  the  author  has  devised  after  very  careful 
study  of  the  subject,  be  compared  with  the  single  straps  as  at  present 
used  in  cotton-mills,  it  will  be  found  that  they  considerably  over- 
shoot the  mark ;  yet,  theoretically,  single  belts,  being  so  much  weaker 


EULES    FOR    BELTING.  27 

and  more  liable  to  stretch  than  double  ones,  ought  to  have  less  strain 
upon  them.  The  secret  of  the  wide  double  driving  belts  running  so 
mysteriously  long  without  attention,  will  at  once  be  seen,  when  it 
is  considered  that  single  belts  are,  as  generally  used,  made  to  drive 
three  or  four  times  more  than  they  ought  to  do  for  their  width  and 
speed. 

"  For  existing  establishments,  where  it  is  not  convenient  to  alter 
the  speed  of  shafting  or  size  of  drums,  in  driving  machines  with  single 
straps,  the  following  will  come  nearer  to  actual  practice. 

Rule  to  find  the  width  of  Belt  fop  any  given  Horse-power. 

"Multiply  33,000  by  the  horse-power  required,  and  divide  the 
product,  first  by  the  length  in  inches  covered  by  the  belt,  and  again 
by  its  speed. 

"  This,  and  more  than  this,  is  what  single  straps  are  made  to  do 
when  driving  machinery.  Comparatively,  then,  the  strong  double 
belts,  working  as  per  first  rule,  have  exceedingly  light  work,  which 
can  be  done  with  great  ease  while  running  in  a  slack  state.  Hence 
their  durability;  and  the  nearer  a  user  of  belts  can  approach  the  rule 
given  for  double  belts,  the  longer  his  straps  will  last." 

Duration  of  Belts. 

#.  "  The  power  is  taken  from  the  jack-shaft  from  pulleys  12  feet 
diameter,  30  inches  face,  and  communicated  direct  to  main  lines  in 
each  room  by  belts  24  inches  wide,  double  leather. 

"These  run  3780  Fpm,  and  are  six  in  number,  driving  from 
highest  to  lowest  power  175  horse  each ;  required  tightening  three 
or  four  times  in  the  first  three  months,  and  never  since.  With 
proper  care,  will  last  20  years;  with  English  leather,  would  last 
much  longer." —  Harmony  Mill,  Cohoes,  N.  Y.,  E.  Leigh. 

"  In  Pittsburgh,  a  20-inch  gum  belt  has  been  in  constant  use  10 £ 
years,  and  notice  is  given  of  three  18-inch  belts  which  have  been 
running  for  9  years." — English  paper. 

Example. 

6.  A  12-inch  belt,  driving  a  5*  feet  pu^ey,  turning  45  Kpm, 
will  carry  away  12  horse-power. 

This  is  the  equivalent  of  64.8  square  feet  of  belt  per  minute  per 
horse-power. 


28  RULES    FOR    BELTING. 

Rule  for  Horse-power  of  Belt. 

„,_  350^ 
~ 


In  which  W=  width  of  belt  in  inches. 

D  =  diameter  of  pulley  in  feet. 

This  gives  a  strain  of  30  Ibs.  per  inch  of  width  of  belt,  and  91.63 
square  feet  of  belt  transmitted  per  horse-power  per  minute. 

Rule. 

8*  "  An  empirical  rule  for  ascertaining  the  width  of  belts  that  we 
know  to  be  in  use  by  some  good  practical  men  is  as  follows  : 

K_S14N 

''~^d~ 

In  which  B  —-  width  of  belt  in  inches,  thickness  taken  at  ^  inch. 

JV  =  number  of  horse-power. 

n  =  number  of  revolutions  per  minute. 

d  =  diameter  of  pulley  in  feet. 

Which  equals  82.163  square  feet  of  belt  in  motion  per  minute  per 
horse-power."  —  Lond.  Mech.  Mag.,  March,  1863. 

Example. 

9.  "A  leather  belt,  19  \  inches  wide,  is  driven  by  a  drum  11  feet 
in  diameter,  having  iron  arms  and  wooden  lagging,  and  making  92 
Rpm;  consequently,  the  belt  moves  at  the  rate  of  3179  Fpm.  The 
amount  of  power  transmitted  by  this  belt  is  estimated  at  175  horse- 
power, corresponding  to  a  tension  of  the  tight  side  of  the  belt  of  not 
less  than 

175  x  38,000 


3179 


=  1817  Ibs. 


The  pulley  driven  by  the  belt  is  6  feet  in  diameter,  and  is  entirely 
of  iron ;  the  peripheries  of  both  drum  and  pulley  are  covered  with 
leather.  The  belt  is  made  of  two  thicknesses  of  leather,  cemented 
together,  and  is  about  |  inch  thick ;  it  was  slightly  greased  on  the 
inside  with  a  mixture  of  tallow  and  neat's-foot  oil.  The  slack  side 
running  upwards  nearly  vertically." 

The  data  above  give  29.5  square  feet  of  belt  per  minute,  per  horse- 
power, and  a  tension  of  93.18  Ibs.  per  inch  wide. 


RULES    FOR    BELTING.  29 

Example. 

10*  "At  a  speed  of  1800  Fpm  on  pulleys  over  36  inches  diam- 
eter, every  one  inch  wide  will  give  2  horse-power." 

This  equals  75  square  feet  per  minute  per  horse-power. 

Example. 

11.  A  certain  6-inch  X  12-inch  cylinder  horizontal  engine,  with 
plain  slide  valve,  arranged  to  cut  off  at  fths  the  stroke,  works  under 
80  pounds  of  steam,  has  a  7-inch  belt  on  a  4-feet  pulley  on  engine 
shaft  making  100  Rpm,  and  drives  a  30-inch  pulley  on  the  "  line " 
shaft  about  4  feet  above  the  cylinder. 

A  24-inch  pulley  on  the  other  end  of  this  "line,"  carrying  a  7-inch 
belt,  with  a  "  half-twist,"  drove  a  10-inch  pulley  on  a  shaft  about  18 
feet  beneath  the  former. 

The  10-inch  pulley  shaft,  in  its  turn,  drove  a  certain  machine, 
which  consumed  more  power  than  the  engine  was  capable  of  giving. 

The  result  was,  the  7-inch  belt  from  the  line  to  the  10-inch  pulley 
would  continue  to  slip,  even  when  very  tight  and  well  covered  with 
rosin,  while  the  7-inch  belt  from  the  line  to  the  pulley  on  the  engine 
shaft  would  hold  firmly  to  its  pulleys,  and  stop  the  engine. 

Crafts  &  Filbert's  Loose  Pulley. 

12.  " The  loose  pulley  shown  herewith  was  patented  Feb.  29, 1876. 

"  Connected  with  machinery  run  at  a  high  rate  of  speed,  loose  pul- 
leys have  been  a  source  of  contin- 
ual  annoyance.     They  not   only 

require  constant  attention,  but  are 
hard  on  the  belt  and  take  much 
oil.  Fig.  4  represents  the  loose 
pulley  2  inches  smaller  than  the 
tight  pulley  and  provided  with  a 
conical  flange  for  the  belt  to  run 
up  on. 

"  The  difference  between  the  pul- 
leys will  slacken  up  the  belt  3 
inches,  taking  the  strain  off  the  Fig.  4. 

belt  and  the  friction  from  the  pul- 
ley, and  allowing  the  belt  to  contract  when  thrown  off  the  tight 
pulley.     The  belt  has  a  chance  to  give  and  take,  as  it  is  always  in  a 
slack  condition  when  on  the  loose  pulley,  and  should  contract  enough 


30  RULES    FOR    BELTING. 

to  keep  it  tight  for  a  loDg  period ;  and  whatever  will  relieve  the  belt 
of  strain  will  add  to  its  durability.  There  is  considerable  wear  and 
tear  on  a  belt  in  shifting  it  with  the  ordinary  pulley.  In  starting  a 
heavy  machine  it  is  necessary  to  hold  the  belt  on  with  the  shifter 
until  the  machine  is  under  full  headway.  During  that  time  the  edge 
of  the  belt  is  rubbing  against  the  shifter,  tearing  up  the  corners  of  the 
laps  and  wearing  away  the  edge  of  the  belt.  But  the  flanged  pulley 
should  require  very  little  aid  from  the  shifter.  When  the  belt  touches 
the  flange  it  immediately  climbs  to  the  tight  pulley,  and  remains 
there  —  starting  the  machine  quickly."  —  The  Polytechnic  Eeview, 
Philadelphia. 

Example. 

13.  The  width  of  a  certain  belt  is  18  inches,  speed  of  same  1500 
Fpm,  angle  of  belt  with  horizon  45°,  distance  between  centres  of 
drums  25  feet,  diameter  of  driving  drum  8  feet,  of  driven  drum  4  feet. 

When  this  belt  transmitted  20  horse-power  it  worked  quite  freely 
and  well ;  when  the  power  was  increased  to  28  horse,  a  tightener  had 
to  be  applied. 

From  the  above  data  we  deduce  the  following  formula : 

HP  x3~ 

=  width  of  belt  in  inches. 


Diam.  small  pulley  in  feet 

If  we  consider  this  belt  as  transmitting  22J  horse-power,  we  shall 
have  a  constant  travel  of  100  square  feet  of  belt  per  minute  per 
horse-power,  assuming  the  above  conditions. — Appleton's  Diet,  of  Mech. 

Example. 

14.  "  A  4-horse  engine  transmits  its  power  through  a  leather  belt 
over  a  cast-iron  pulley  4  feet  diameter,  running  100  Rpm,  and  em- 
bracing .4  of  its  circumference. 

"  In  this  example  the  thickness  of  belt  is  taken  at  .15  inch,  and 
the  strain  at  210  Ibs.,  which  gives  4.67  inches  for  width  of  belt,  and 
122.26  square  feet  of  belt  per  minute  per  horse-power,  or  101.88  square 
feet,  when  .5  of  the  circumference  of  pulley  is  embraced,  using  Morin's 
ratio  of  2  :  2.4.  If  thickness  of  belt  be  taken  at  -f^  inch,  and  half 
the  circumference  be  embraced  by  belt,  then  we  have  81.375  square 
feet  per  minute  per  horse-power. 

"An  11-inch  belt  on  a  4-feet  pulley  running  from  1200  to  2100 
Fpm  will  transmit  the  power  of  a  double  steam-engine  with  6-inch 


RULES    FOR    BELTING.  31 

X  11-inch  cylinders,  125  Rpm,  under  a  steam  pressure  of  60  Ibs.  per 
square  inch."  —  Haswell,  1867. 

Example. 

15,  A  single  leather  belt  in  good  driving  condition  has  been  fre- 
quently used  in  testing  car-wheel  forcing-presses.  Under  the  follow- 
ing conditions  this  belt  was  repeatedly  found  to  just  do  the  work: 
Belt  6  inches  wide,  pulley  24  inches  diameter,  of  iron,  smooth  turned, 
crank  2  inches  radius,  plunger  -]f  inch  diameter  in  a  1{  inch  barrel, 
hydraulic  pressure  7000  Ibs.  per  square  inch  ;  hence  we  have  : 

(area  of  ll  inches  —  area  of  §)  7000 

\  _  J      *  J   16J  1n,  &s> 

~6^T  =104JKt' 

From  this  we  may  safely  conclude  the  maximum  driving  force  of  a 
single  leather  belt  to  be  near  100  Ibs.  per  inch  of  width.  —  A.  B.  Couch. 

16.    Molesworth's  Pocket-  Book  of  Engineering  Formulae. 
17th  Edition,  London,  1875. 

Leather  Belting. 

V=  velocity  of  belt  in  feet  per  minute. 
HP—  horse-power  (actual)  transmitted  by  belt. 
S  —strain  on  belt  in  Ibs. 
W=  width  of  single  belting  (T3g  thick)  in  inches. 


33,000  HP 

-v— 

k  =  1.1,  .77,  and  .62  when  portion  of  driven  pulley  embraced 
by  belt  =  .40,  .50,  and  .60  of  the  circumference,  respectively. 
For  double  belting  the  width  —  W  X  .6. 
Approximate  rule  for  single  belting  -f%  thick  : 


"  The  formulse  above  apply  to  ordinary  cases,  but  are  inapplicable 
to  cases  in  which  very  small  pulleys  are  driven  at  very  high  velocities, 
as  in  some  wood-cutting  machines,  fans,  etc.  The  acting  area  of  the 
belt  on  the  circumference  of  the  driven  pulley  being  so  small  that 


32  RULES    FOR    BELTING. 

either  great  tension  or  a  greater  breadth  than  that  determined  by  the 
formula  is  required  to  prevent  the  belt  from  slipping. 

"  In  such  extreme  cases  of  high-speed  belts,  find  the  breadth  of 
the  first-motion  belt,  by  the  formula  for  ordinary  belting  above  (a), 
then  if  — 

A  —  acting  area  of  first-motion  belt. 
v  =  velocity  of  first-motion  belt. 
a  =  acting  area  of  high-speed  belt. 
V=  velocity  of  high-speed  belt. 
Av 


"  The  acting  area  of  either  belt  =  I  x  b. 

Where  £  =  length  of  circumference  of  driven  pulley  embraced  by  the 
belt, 

b  =  breadth  of  the  belt. 

.*.  b  =  —  in  the  case  of  the  high  speed  belt. 

"If  there  is  no  first-motion  belt  exclusively  for  the  machine,  it 
will  be  easy  to  suppose  a  hypothetical  case  from  which  the  breadth 
of  the  high-speed  belt  may  be  calculated." 

Kule  (a)  is  the  equivalent  of  91|  square  feet  of  belt  per  minute 
per  horse-power. 

Rule. 

17  '•  Several  years  of  satisfactory  use  of  a  table  which  purports  to 
give  reliable  data  about  belts,  would  seem  to  clinch  the  truth  of  size 
for  power,  and  to  show  its  value,  we  take  from  it  a  6-inch  belt  run- 
ning 2200  Fpm,  and  find  it  capable  of  doing  12|  horse-power,  which 
is  the  equivalent  of  89.8  square  feet  per  minute  per  horse-power. 

Rule. 

18*  A  rule  to  find  the  power  of  a  belt  may  be  stated  thus  :  Di- 
vide 1070  into  the  product  of  the  belt's  width  in  inches,  by  its  veloc- 
ity in  Fpm,  which  proves  it  the  equivalent  of  89.17  square  feet  of 
surface  velocity. 

Rule. 

19.    Another  takes  this  shape  : 

HP  5400 
V  d 


RULES    FOR    BELTING.  33 

In  which  W=  width  of  belt  in  inches. 
"        HP  —  horse-power. 

"  y=  velocity  of  belt  in  feet  per  minute. 

"  d  =  diameter  of  smaller  pulley  in  feet. 

This  rule  is  handed  down  to  us  by  a  good  engineer,  who  used  it 
with  success  for  many  years ;  it  has  also  the  advantage  of  giving  a 
margin  of  25  per  cent,  of  adhesion  before  slippage  will  take  place. 

Example. 

20.  An  horizontal  non-condensing  engine,  with  a  cylinder   12 
inches  diameter,  30  inches  stroke,  running  66  Rpm,  under  72  pounds 
of  steam  in  boiler,  and  an  average  pressure  of  19.7  pounds  of  steam 
on  piston,  has  a  13^-inch  belt  on  an  8-feet  fly-wheel  pulley,  which 
runs  over  a  4-feet  pulley  on  a  shaft  18  feet  vertically  above.     Speed 
of  belt  1658.58  Fpm.     On  one  occasion  the  indicator  showed  21 
horse-power  transmitted ;  this  would  give  88.85  square  feet  of  belt 
per  horse-power  per  minute. 

Example. 

21.  An  engine  similar  to  that  above,  with  10  inches  X  24  inches 
cylinder,  making  80  Rpm,  under  100  pounds  of  steam  in  the  boiler, 
and  showing  by  the  indicator  a  constant  work  of  33  horse-power,  has 
a  11^-inch  belt  on  a  5-feet  pulley  on  engine  shaft.     This  belt  is 
crossed  and  runs  over  a  34-inch  pulley  on  the  "line"  shaft  8  feet 
above  and  18  feet  distant.     Number  of  square  feet  of  belt  trans- 
mitted per  horse-power  per  minute  36.5.     Speed  of  belt  1256  feet 
per  minute. 

Example. 

22.  An  engine  with  steam  cylinder  15  inches  diameter,  36  inches 
stroke ;  fly-wheel  pulley  12  feet  diameter,  carrying  a  17A-inch  belt, 
which  passes  over  a  5-feet  pulley,  6  feet  above  and  18  feet  6  inches 
distant ;  top  fold  of  belt  slack. 

Engine  makes  48  Rpm  under  65  pounds  of  steam,  and  by  the 
indicator  shows  a  work  done  of  40.7  horse-power.  Speed  of  belt 
1809.12  per  minute,  and  square  feet  of  belt  transmitted  64.61  per 
horse-power  per  minute. 

Example. 

23.  An  horizontal  non-condensing  engine,  with  11  inches  X  30 
inches  cylinder,  arranged  with  two  steam  and  two  exhaust  valves  of 


34 


KULES    FOR    BELTING. 


the  double  beat  balanced  Cornish  style,  each  operated  by  a  cam,  the 
two  former  under  the  control  of  the  governor.  A  10-feet  fly-wheel 
pulley  carries  a  20-inch  single  leather  belt.  On  the  line  shaft  6  feet 
above  and  15  feet  distant  is  a  5-feet  pulley,  the  belt  passes  over  this 
pulley,  the  top  fold  running  slack.  Under  80  pounds  of  steam  in  the 
boiler  a  pressure  of  60J  pounds  per  square  inch  on  the  piston  is  main- 
tained to  the  point  of  cut-off,  which  was  one-third  the  stroke  on  one 
occasion  when  the  indicator  showed  a  work  of  29.27  horse-power; 
speed  of  engine  56  Kpm.  The  load  of  this  engine  is  very  variable ; 

the  average  of  a  number 
of  cards  taken  shows  25 
horse-power.  Speed  of 
belt  1758.4  Fpm,  and 
number  of  square  feet 
of  belt  per  horse-power 
per  minute  transmitted 
117.2. 

Example. 

24. .  A  20-inch  x  48- 
inch  cylinder  horizontal 
non  -  condensing  engine 
has  a  16-feet  fly-wheel 
pulley  carrying  a  24- 
inch  belt,  and  runs  about 
50  Rpm.  This  beJt 
drives  a  5-feet  4-inch 
pulley,  32  feet  distant  in 
an  angle  of  about  40°, 
the  top  fold  slack.  By 
the  indicator  the  engine 
is  working  up  to  150 
horse-power.  Speed  of 
belt  2513  Fpm,  and 
square  feet  transmitted 
per  minute  per  horse- 
power equals  33.5. 


Fig.  5. 


Example. 

25 •    An  18-inch  x  36-inch  engine,  having  a  14- feet  8-inch  fly-wheel 
pulley,  making  52  Rpm,  carries  two  belts  (see  Fig.  5)  ;  a  15-inch  run- 


RULES    FOR    BELTING.  35 

ning  over  a  5-feet  pulley  directly  above,  45  feet  distant,  and  a  16-inch, 
running  over  a  6- feet  pulley  20  feet  distant,  at  an  angle  of  about  30°. 
This  engine,  under  a  boiler  pressure  of  85  Ibs.,  shows  by  the  indi- 
cator, 114.6  horse-power.  Speed  of  belts  2392  Fpm,  and  square  feet 
of  belt  transmitted  per  minute  per  horse-power  54. 

Example. 

26*  A  14-inch  by  36-inch  cylinder  engine  has  a  12-feet  fly-wheel 
pulley  carrying  an  18-inch  belt,  tight  fold  below,  at  an  angle  of  about 
30°.  Pulley  on  line  shaft  6  feet  diameter,  and  about  25  feet  distant. 
Speed  of  engine  56  Rpm.  Horse-power  by  the  indicator  49.  Speed 
of  belt  2111.2  Fpm,  and  square  feet  per  horse-power  per  minute 
64.63. 


Fig.  6. 

From  J.  W.   Nystrom's  "  Elements  of  Mechanics.'* 
Philadelphia,  1875. 

27.  "  The  best  and  simplest  mode  of  transmitting  motion  from  one 
shaft  to  another,  is  by  a  belt  and  pulleys,  which  is  very  extensively 
used,  and  it  gives  the  smoothest  motion.  The  motion  is  transmitted 
by  the  frictional  adhesion  between  the  surfaces  in  contact  of  the  belt 
and  pulleys,  for  which  reason  that  friction  must  be  greater  than  the 
tension  of  the  belt ;  otherwise  the  belt  will  slip  and  fail  to  transmit 
all  the  motion  due  from  the  driving  pulley.  There  is  always  some 
slip  in  belt  and  pulleys,  for  which  reason  that  mode  of  transmission 
is  not  positive  or  exact,  and  cannot  be  used  where  precise  motions  are 
required. 


36  RULES    FOR    BELTING. 

"Fig.  6  represents  a  belt  transmitting  motion  between  two  parallel 
shafts,  a  and  b.  If  the  motion  is  transmitted  from  a  to  b,  the  pulley 
D  is  called  the  driving  pulley,  and  d  the  driven  pulley.  The  diam- 
eters of  the  pulleys  can  be  of  any  desired  proportions  to  suit  the  work 
of  the  machine. 

D  =  diameter,  and  It  =  radius  in  inches  of  the  driving  pulley. 
d  =  diameter,  and  r  =  radius  of  the  driven  pulley. 
L  =  length,  and  B  =  breadth  of  the  belt  in  inches. 
F  =  force  of  tension  in  pounds  of  the  pulling  side  of  the  belt. 
/  =  force  of  tension  on  the  slack  side. 
V=  velocity  of  the  belt  in  feet  per  second. 
S  =  distance  in  inches  between  the  centres  of  the  two  pulleys. 
N  and  n  =  numbers  of  revolutions  per  minute  of  the  respective 

pulleys,  D  and  d. 

$  =  angle  in  degrees  occupied  by  the  belt  on  the  small  pulley. 
HP=  horse-power  transmitted  by  the  belt. 

"  Revolutions  N  :  n  =  d  :  D,  diameters.  The  revolutions  are  in- 
verse as  the  diameters. 

nd  ND  ND  dn 


"  The  force  bearing  in  the  journals  of  each  shaft  is  JF  -f  /,  or  the 
sum  of  the  tensions  of  each  side  of  the  belt. 

"  The  force  which  transmits  the  motion  is  F  —  /,  or  the  difference 
between  the  two  tensions. 

"  The  effective  power  transmitted  is  equal  to  the  product  of  the 
transmitting  force  and  the  velocity,  and  this  power  divided  by  550 
gives  the  horse-power. 

"  The  length,  L,  of  the  belt  will  be  found  by  the  following  formula: 


L  =  «  (E  -f-  r)  +  2  ^/S*  -f  (R  —  rJ. 

"  When  the  diameters  of  the  pulleys  are  alike,  or  D  =  d,  the  length 
of  the  belt  will  be 

L  =  x  D  -f  2  S. 

"  The  slip  of  belt  on  equal  pulleys  has  been  found  by  experience 
to  vary  between  2  and  3  per  cent,  under  ordinary  circumstances. 


RULES    FOR    BELTING. 


37 


n  =  theoretical  revolutions  per  minute  of  the  driven  pulley. 
n'=  actual  revolution  after  the  slip  is  deducted. 


n'= 


182 


Formulas  for  Leather  Belts  on  Cast-iron  Pulleys. 
Force  and  Power  of  Transmission.      Breadth  of  Belts  from  Experiments. 


1. 


3. 


7?       f 

jLXOOUU  HIT 

Q                ^              /  /  /  OUU  J3.JT 

*       J 

*-/- 

F      f 

d  n 
126500  HP 

n  d  <j> 
94  F 

D  N 
550  HP 

d 

/  QO      XT' 

11                7?         ^ 

f      J 
HP 

V 

elt 

^^  HP 

550 

d  n  (F-f) 

nd 

13          R      7'*-F'F 

126500 

n  d 
Bnd 

y 

126500 
dn      D  N 

14.     Jii  —  

4320 

15      ^p       Bnd* 

W  

230       230 
126500  HP 

777600 
F     Bd 

d  (F-f) 

2.4 

5. 


6. 


7. 


8. 


Treatment  and  Condition  of  Leather  for  Belts. 

28.  "  I  stuff  my  belts  with  a  composition  of  two  pounds  of  tallow, 
one  pound  of  bay-berry  tallow,  and  one  pound  of  beeswax,  heated  to 
the  boiling-point,  and  applied  directly  to  both  sides  by  a  brush,  after 
which  the  belts  are  held  close  to  a  red-hot  plate  to  soak  the  beeswax 
in,  which  does  not  enter  the  pores  of  the  leather  from  the  brush." 


38  RULES    FOB    BELTING. 

"  Care  must  be  taken  to  have  the  leather  perfectly  dry  to  prevent 
burning.  I  placed  a  kettle  of  the  composition  over  a  blacksmith's 
fire,  and  after  melting  it,  I  put  in  a  coil  of  2-inch  belting  about  16 
feet  long,  and  boiled  it  45  minutes  in  the  greatest  degree  of  heat  I 
could  produce  by  blowing  the  fire  continually,  and  the  belt  when 
taken  out  was  not  in  the  least  injured  by  the  heat  of  the  composition. 
I  then  tried  a  piece  of  belting  damped  with  water,  and  found  it  burnt 
and  crisped  in  less  than  half  a  minute." 

"  The  application  of  neat's-foot  oil  to  belts,  opens  the  pores  of  the 
leather,  and  destroys  the  adhesion  of  its  parts,  and  in  a  very  short 
time  renders  it  flaccid  and  rotten,  and  a  belt  will  not  last  half  so 
long  stuffed  with  oil  as  with  the  composition  above  named.  Belts 
stuffed  with  the  composition  are  impervious  to  water,  and  will  run 
well  for  six  months." — /.  H.  B.,  Frank.  Ins.  Jour.,  June,  1837. 

"  Fat  should  be  applied  to  belts  once  every  three  months.  They 
should  be  first  washed  with  lukewarm  water,  and  then  have  leather- 
grease  well  rubbed  in.  A  good  leather-grease  may  be  made  from 
fish-oil,  4  parts;  lard  or  tallow,  1  ;  colophonium,  1 ;  wood-tar,  1." — 
Workshop  Receipts,  by  Ernst  Spon,  London,  1875. 

Leather  belts  may  be  kept  in  good  working  condition  by  the  judi- 
cious use  of  fish-oil,  mixed  with  spent  -grease  of  journal-boxes,  and 
also  by  neat's-foot  oil,  which  may  be  applied  by  a  brush  two  or  three 
times  swept  over  after  the  belt  has  been  soaked  some  ten  minutes  in 
water. 

Whitaker's  castor-oil  dressing  is  one  of  the  best  modern  adhesives 
for  leather  belts. 

"  In  order  that  belting  of  cotton  or  linen  should  have  both  strength 
and  flexibility,  together  with  increased  adhesive  power,  they  should 
be  thoroughly  soaked  in  linseed -oil  varnish.  If  the  belting  be  new, 
the  varnish  may  be  applied  with  a  brush,  until  no  more  will  be  taken 
up,  whereupon  it  may  immediately  be  used  without  any  preparatory 
drying.  After  having  been  in  use  for  some  weeks,  a  second  appli- 
cation of  the  varnish  should  be  put  on.  Cotton  or  linen  belting  thus 
prepared  will  neither  contract  nor  stretch,  and  will  always  be  pli- 
able and  unaffected  by  change  of  temperature.  The  adhesion  of  the 
belt  to  the  pulley  is  likewise  increased  by  the  varnish,  while  steam 
and  acid  fumes  have  no  effect  upon  the  belting  at  all."  —  Polytechnic 
Review. 

Belts  stuffed  with  tanners'  dubbing  on  the  flesh  side,  will  become 
as  smooth  as  the  hair  side,  and  will  outlast  six  belts  which  are  run 
on  the  hair  side  exclusively. 


RULES    FOR    BELTING.  39 

Frequent  application  of  neat's-foot  oil  promotes  regularity  of  speed, 
durability  of  leather,  and  economy  of  use. 

Three  times  the  adhesiveness  is  gained  by  softness  and  pliableness 
of  belting  leathers  over  those  which  are  dry  and  husky. 

A  right  good  way  to  oil  a  belt  is  to  unreel  from  one  coil  to  another, 
allowing  the  loose  fold  to  draw  through  a  pot  of  oil,  with  rubbers  at 
the  outgoing  part  to  wipe  back  the  superfluous  grease. 

"  Keep  belts  clean  by  washing  them  with  warm  water  and  soda, 
scrape  them  well  and  apply  freely  the  spent  grease  of  journal  boxes." 

Influence  of  the  Thickness  of  Belts. 

29.  "  When  bent  round  the  circumference  of  a  wheel,  the  outer 
parts  of  the  belt  are  distended,  the  inner  parts  relaxed ;  and  sup- 
posing the  section  of  the  belt  to  be  rectangular,  the  amount  of  force 
expended  in  making  these  changes  is  proportional  directly  to  the 
breadth,  to  the  square  of  the  thickness,  and  inversely  to  the  diameter 
of  the  wheel.     Hence  if  two  belts  be  of  like  strength,  but  the  one 
broad  and  thin,  the  other  narrow  and  thick,  the  amounts  of  force 
expended  in  bending  them  must  be  proportional  directly  to  their 
thicknesses,  and  hence  the  advantage  of  using  broad  thin  belts." . 

"  The  practice  of  strengthening  belts  by  riveting  on  an  additional 
layer  must  be  exceedingly  objectionable :  indeed,  it  is  difficult  to  see 
how  any  additional  strength  is  gained,  for  the  outer  layer  must  be 
tight  when  on  the  wheel,  and  slack  when  free,  so  that  in  reality,  the 
strength  of  only  one  layer  can  be  available,  the  parts  of  the  com- 
pound belt  are  puckered  and  opened  alternately,  as  evinced  by  the 
crackling  noise." 

"  The  proper  procedure  is  to  increase  the  breadth  of  the  belt." 
"  So  far  as  we  have  yet  seen,  it  is  preferable  to  use  heavy  belts." — 
Prac.  Mech.  Journal,  November,  1866,  p.  240. 

Variation  of  Speed. 

30.  From  experiments  made,  it  has  been  ascertained  that  about 
two  revolutions  per  hundred  are  lost  in  the  transmission  of  motion 
by  a  belt.     In  ordinary  practice  this  would  be  a  slight  loss,  and 
would  in  no  wise  interfere  with  the  usual  manufacturing  processes, 
but  where  there  is  a  long  train  of  gear  repeated  from  shaft  to  shaft 
by  belts,  the  loss  becomes  serious. 

It  is  clear  if  the  co-efficient  of  loss  by  slippage  be  .98  for  a  single 
pair,  which  has  been  verified  with  great  certainty  by  varying  the 
tensions  of  the  same  belt,  it  will  become  equal  to  the  successive 


40  KULES    FOR    BELTING. 

powers  :  .98,  .96,  .94,  .92,  .90,  and  so  on  ;  so  that  after  a  succession 
of  five  speeds  the  loss  amounts  to  y^th  of  the  calculated  speed,  and 
that  at  the  end  of  thirty-four  speeds  the  velocity  will  be  reduced  to 
half. 

From  these  considerations  it  appears  that  where  it  is  required  to 
transmit  speeds  as  near  determinate  as  may  be,  by  means  of  bands 
and  pulleys  it  is  necessary  to  increase  the  diameter  of  the  driving 
pulley  by  its  fiftieth  part,  or  diminish  the  driven  pulley  in  the  same 
ratio.  —  See  Lond.  Mech.  Mag.,  March,  1863. 

Prof.  L.  G.  Franck,  in  Jour,  of  Franklin  Inst.  (May,  1875),  gives  a 
theory  of  the  tension  of  belts,  from  which  we  take  the  following. 

31.  "  The  tension  of  the  belt  is  counteracted  by  the  cross-section 
of  the  belt,  that  is  2.4/S  =  wtK,  where  w  denotes  the  width  of  the 
belt,  t  the  thickness,  both  given  in  inches,  and  K  the  number  of 
pounds  which  one  square  inch  of  belt  will  fairly  resist,  found  by  ex- 
periment. From  equation  (5),  in  article  referred  to,  we  have 


which,  if  introduced  into  the  above  equation  and  solved  with  respect 
to  w,  will  give 


"  In  general  M  is  not  directly  known,  but  the  number  of  horse- 
powers the  pulley  shall  transmit  is  given,  and  the  number  of  Rpm 
of  the  pulley,  or  the  number  of  feet  that  the  belt  travels  per  minute. 
From  these  data  we  are  enabled  to  express  S.  Putting  formula  (1) 
in  the  form 


tK' 

the  dynamical  effect  of  S  for  n  revolutions  in  one  minute  is  expressed. 

"  Number  of  horse-powers  =  N=  —      —> 

33000 

from  which  we  get 

33000N 

o  = 


RULES    FOB    BELTING.  41 

which  when  introduced  into  equation  (2)  gives 

2.4xS3000N 


w  — 


2*RntK 


where  w  denotes  the  width  of  the  belt  in  inches,  N  the  number  of 
horse-powers,  R  the  radius  in  feet,  n  the  number  of  revolutions,  t  the 
thickness  of  the  belt,  and  K  the  resistance  expressed  in  pounds 
which  one  square  inch  of  belt  can  fairly  counteract.  Taking  t  = 
1%-  inches,  and  for  K,  after  Morin,  275  pounds.  K  depends  on  the 
quality  of  the  leather,  and  ranges  from  275  to  550  pounds  per  square 
inch.  275  pounds  are  recommended,  however,  by  good  authorities. 
Applying  the  latter  we  shall  find,  after  reducing  the  above  numerical 
values, 

W  =  ™»  (3) 

nR 

where  the  numerical  value  is  rounded  off  to  an  even  number. 

Example  I. 

"A  pulley  of  1£  feet  radius  makes  80  Rpm,  having  to  transmit 
one  horse-power.     What  should  be  the  width  of  the  belt  ? 

Here  N=  1;  n  =  80,  and  R  =  l\. 

250          25       „!   . 

Hence  W  =  -      -  =  •  —  =  2  ~  inches. 
80*1       12          * 

Example  2. 

"A  pulley  of  3  inches  radius  makes  900  Rpm,  and  has  to  trans- 
mit 2  horse-powers.     What  should  be  the  width  of  the  belt  ? 

N=2;  n  =  900;  R  =   fl. 


900  Xj 

"  Solving  equation  (3)  with  respect  to  JV,  we  find  : 

N=^^.  (4) 

250 

"  Giving  to  w  the  exceptional  width  of  6  inches  for  a  single  belt, 
and  assuming  n  =  100  Rpm,  and  further  the  radius  of  the  pulley 
R  =  1  foot,  we  find  the  number  of  horse-powers  : 


250 


42  RULES    FOR    BELTING. 

"  The  number  of  horse-powers  that  are  obtained  is  comparatively 
small,  and  it  indicates  that  with  pulleys  and  belts  we  cannot  produce 
a  very  great  effect  unless  we  make  the  radius  of  the  pulley  very  great, 
and  apply  an  exceptionally  great  speed. 

"  I  should  mention  that  the  above  formulae  refer  to  pulleys  with 
open  belts  only,  and  that  it  is  of  no  consequence  whether  the  radius 
and  respective  number  of  revolutions  are  taken  from  the  greater  or 
smaller  pulley,  as  the  numbers  of  revolutions  are  in  an  inverse  ratio 
to  the  radii  of  the  pulleys.  That  is : 

—  —  — -.     Hence,  R  n  =  Rt  ??,. 
Hi        n 

"  If  the  belt  is  made  up  of  two  layers  or  thicknesses,  so  that  such 
a  belt  of  the  same  width  as  a  single  one  contains  the  double  cross- 
section,  we  still  may  apply  the  upper  formula,  if  we  multiply  it  by  f , 
owing  to  the  greater  stiffness  of  the  belt. 

Example. 

"  In  order  to  transmit  4  horse-powers,  we  have  a  pulley  1  ft.  8  in. 
by  120  Kprn.  What  should  be  the  width  of  the  belt? 

N=4;  It  =  lift.;  n=120. 

2    250  N      ,250x4        9 
W=s  ~~s  -  =  3 

nR        S      120  x5- 

3 

"  For  the  single  belt  we  should  have  received  : 
W=l  X3l  =  5  inches." 

NOTE  1. — "As  great  nicety  is  not  required  in  these  calculations, 
the  co-efficient  of  friction  may  be  taken  in  general  as  0.25  and  the 
arc  covered  by  the  belt  as  T4^-  of  the  circumference  of  the  smaller 
pulley." 

NOTE  2. — The  reader  should  observe  that  the  figures  of  these  ex- 
amples show  a  velocity  area  of  the  belt  of  130.83  square  feet  per  minute 
per  horse-power,  which,  with  good  single  leather  belts  in  fair  working 
condition,  is  an  allowance  of  nearly  double  the  quantity  needed  under 
ordinary  circumstances,  for  proof  of  which  see  other  articles. 


RULES    FOR    BELTING.  43 

Running  Conditions. 

32.  "  The  slack  side  on  top,  with  large  pulleys  at  high  speed,  is 
undoubtedly  the  true  philosophy  of  transmitting  power  by  belts." 

Not  speed  alone  but  adhesive  force  must  be  gained  to  do  work 
without  destructive  tightness  or  slippage  of  the  belt,  therefore,  there 
should  be  a  proper  proportion  of  pulley  diameter  and  belt  contact. 

Long  belts  are  preferred  to  short  ones,  but  care  must  be  taken  that 
the  length  be  not  too  great. 

We  have  a  case  in  point  where  a  60-inch  pulley  at  45  Rpm  drove 
a  15-inch  pulley,  about  50  feet  distant,  by  an  11-inch  belt,  109  feet 
long.  The  tops  of  the  pulleys  were  nearly  on  the  same  level,  and  the 
belt  was  crossed. 

This  belt  was  continually  flapping  about,  soon  became  crooked  and 
irregular  in  width,  and  was  frequently  torn  asunder  at  the  lacings  by 
excessive  tension,  and  the  whole  arrangement  proved  very  trouble- 
some until  changed  to  the  following :  The  speed  of  the  60-inch  and 
the  diameter  of  the  driven  pulley  were  doubled,  and  the  distance  be- 
tween their  centres  was  reduced  to  15  feet.  The  belt  now  drives  with 
more  power,  gives  greater  regularity  of  speed,  and  works  better  every 
way. 

Another  case  of  excessive  length,  which  has  come  under  our  notice, 
is  that  of  an  11-inch  open  belt  on  a  4-feet  pulley,  running  horizon- 
tally at  a  speed  of  2261  Fpm  over  a  32-inch  pulley,  30£  feet  distant. 
To  prevent  surging,  this  belt  must  be  drawn  and  laced  very  tightly ; 
too  much  so  for  economical  running. 

Some  facts  illustrating  the  evils  of  short  belts  were  given  to  me  by 
a  friend. 

A  30-inch  pulley,  running  127  Rpm,  drove  a  9-inch  pulley  by  a 
5-inch  belt  14  feet  long,  the  shafts  were  nearly  in  a  horizontal  plane, 
and  the  lower  fold  of  the  belt  did  the  driving. 

To  do  a  certain  woik  this  belt  frequently  slipped,  even  when  tightly 
drawn,  so  much  so  that  it  tore  out  at  the  lacings  almost  daily,  and 
sometimes  three  times  a  day. 

After  much  inconvenience  it  was  changed  for  a  belt  44  feet  long ; 
the  9-inch  pulley  shaft  being  removed  horizontally  to  accommo- 
date the  increased  length,  while  all  the  other  parts  remained  the 
same. 

It  now  performs  most  satisfactorily ;  it  does  not  slip,  holds  at  the 
lacings,  and  the  slack  fold  above  sometimes  nearly  touches  the  driving 
one  beneath. 


44  RULES    FOE    BELTING. 

The  9-inch  pulley  shaft  carries  an  18-inch  pulley,  which,  in  its  turn, 
drives  a  7-inch  pulley  below  on  an  Alden  fan  spindle. 

"  A  belt  adheres  much  better  and  is  less  liable  to  slip  when  at  a 
quick  speed  than  at  a  slow  speed.  Therefore  it  is  better  to  gear  a 
mill  with  small  drums,  and  run  them  at  a  high  velocity,  than  with 
large  drums,  and  to  run  them  slower ;  and  a  mill  thus  geared  costs 
less  and  has  a  much  neater  appearance  than  with  large,  heavy  drums ; 
and  in  belting,  if  the  power  of  a  belt  18  inches  wide  were  required, 
it  would  be  better  to  put  in  two  9-inch  belts  than  one  so  wide,  owing 
to  the  greater  inequalities  of  leather  in  such  large  pieces  causing  loss 
of  adhesion."—/.  H.  £.,  in  Frank.  Inst.  Jour.,  June,  1837. 

Convexity  of  Pulleys. 

33.  Morin  says .  "  The  pulleys  over  which  leather  belts  pass  ought 
to  have  a  convexity  equal  to  about  -^  of  their  breadth." 

London  Mech.  Mag.  for  March,  1863,  says :  "  Belt  pulleys  should 
be  made  slightly  convex,  in  a  ratio  of  ^  inch  per  foot  of  breadth." 
Molesworth  says  the  same. 

Another  proportion  is  %  inch  rise  in  8  inches  of  width.  Still 
another,  ^  inch  to  the  foot. 

"The  rounding  should  be  made  as  slight  as  is  consistent  with 
security,  since  every  deviation  from  the  cylindric  form  is  accompanied 
by  a  loss  of  force." 

"  In  their  progress  round  the  wheels,  the  different  parts  of  the  belt 
are  stretched  and  relaxed  alternately.  Now,  if  the  material  were 
perfectly  elastic,  the  force  expended  on  the  distension  would  be  repro- 
duced on  the  contraction  of  the  belt.  As  the  loss  by  this  imperfect 
elasticity  is  not  known,  it  will  be  enough  to  observe,  for  the  present, 
that  the  loss  of  force  will  certainly  be  greater,  the  greater  the  dis- 
turbance of  the  particles  —  the  higher  the  rounding  of  the  pulleys." 

Why  a  Belt  Runs  to  the  Higher  Part  of  a  Pulley. 

34*  Much  disputation  has  been  published  in  efforts  to  solve  the 
question :  Why  does  a  belt  run  to  the  higher  part  of  a  pulley  ?  There 
may  be  several  causes,  but  the  chief  one  is  embodied  in  the  following 
words :  "  That  edge  of  the  belt  which  is  towards  the  larger  end  of  the 
cone  is  more  rapidly  drawn  than  the  other  edge ;  in  consequence  of 
this  the  advancing  part  of  the  belt  is  thrown  in  the  direction  of  the 
larger  part  of  the  cone,  which  obliquity  of  advance  towards  the  cone 
must  lead  the  belt  on  its  higher  part. 

"  It  may  here  be  observed  that  this  very  provision  —  the  rounding 


RULES    FOR    BELTING.  45 

of  the  face  of  the  pulley  —  which  keeps  the  belt  in  its  place  so  long 
as  the  machinery  is  in  proper  action,  tends  to  throw  it  off  whenever 
the  resistance  becomes  so  great  as  to  cause  a  slipping." 

"  To  maintain  a  belt  in  position  on  a  pulley,  it  is  necessary  to  have 
the  advancing  part  in  the  plane  of  the  wheel's  rotation." 

Superiority  of  the  Driving- Belt. 

35.  "  There  is  no  simpler  or  smoother  means  of  communicating  mo- 
tion than  that  afforded  by  the  noiseless  agency  of  cords,  bands,  or  straps. 
The  very  means  by  which  the  motion  is  maintained — namely,  by  the 
frictional  adhesion  between  the  surfaces  of  the  belt  and  the  pulley  — 
is  a  safeguard  to  the  whole  mechanism,  as,  if  any  unusual  or  acci- 
dental obstruction  should  intervene,  the  belt  merely  slips,  and  break- 
age and  accident  are  thus  prevented." — London  Mech.  Mag.,  March, 
1863. 

"The  facility  with  which  this  communication  of  rotary  motion 
may  be  established  or  broken  at  any  distance,  and  under  almost 
every  variety  of  circumstance,  has  brought  the  band  so  extensively 
into  use  in  machinery,  that  it  may  be  considered  as  one  of  the  prin- 
cipal channels  through  which  work  is  made  to  flow." — Moseley. 

Covering  for  Pulleys. 

30.  Pulleys  may  be  well  covered  in  the  following  manner:  — 
Take  a  piece  of  belt-leather  of  uniform  thickness  the  width  of  pulley 
face,  and  of  a  length  equal  to  circumference  of  pulley,  plus  the  lap, 
but  less  |  inch  for  every  foot  of  diameter  of  the  pulley,  then  scarf 
and  unite  the  lap  so  as  not  to  increase  the  thickness  when  cemented 
together.  When  ready  for  use  draw  the  covering  on  by  means  of 
iron  hooks,  observing  to  put  hair  side  out  and  so  that  outer  end  of 
lap  will  not  be  raised  when  covering  slips  under  the  belt.  Secure  to 
the  pulley  rim  by  copper  rivets,  sinking  heads  beneath  the  driving 
surface. 

The  laps  of  all  belts  should  be  disposed  in  a  similar  way. 

Effect  of  Disproportion  of  Connected  Machinery. 

37.  Sometimes  a  belt  works  badly  from  causes  outside  of  its  own 
motion  and  proportions. 

We  have  a  case  in  practice  which  will  forcibly  illustrate  this.  A 
46-inch  pulley,  on  the  "  line  "  shaft,  drives  a  5- feet  pulley  on  a  4-inch 
shaft,  at  the  rate  of  73  Rpm,  by  a  12-inch  open  belt.  This  shaft  is 
7  feet  8  inches  below,  and  2  feet  aside  of  the  "  line  "  shaft,  and  car- 


46  RULES    FOR    BELTING. 

ries  an  8-feet  fly-wheel  of  3750  Ibs.  weight  on  its  middle,  and  a  crank, 
with  a  double  pin,  on  its  overhanging  end,  which  latter  is  connected 
with  and  drives  two  marble  saw-frames,  one  very  heavy,  the  other  of 
medium  size.  The  belt  runs  slack  and  free,  and  has  not  been  touched 
at  the  lacings  during  six  months  of  very  steady  and  satisfactory 
running. 

Before  the  8-feet  fly-wheel  was  put  on,  a  6-feet  fly-wheel,  of  about 
1450  Ibs.  was  used,  which  a  long,  troublesome  experience  proved 
altogether  inefficient.  The  belt  had  to  be  run  very  tightly ;  it  tore 
frequently  at  the  lacings — even  when  the  laced  ends  were  doubled  to 
make  the  stronger  joining  —  and  at  all  times  while  running  the  lack 
of  momentum  of  the  wheel  caused  unsteadiness  of  motion  in  the  whole 
system  of  gearing  in  the  mill. 

Care  of  Belts. 

38*  In  order  to  have  belts  run  well,  they  should  be  perfectly 
straight  and  be  of  equal  thickness  throughout  their  length,  have  but 
one  laced  joint ;  but  if  circumstances,  require  any  belts  to  be  com- 
posed of  several  pieces,  the  ends  should  be  evenly  bevelled,  and  united 
by  one  or  other  of  the  permanent  ways  mentioned  hereafter.  The  ends 
to  be  laced  should  be  cut  at  right  angles  to  the  sides,  the  lace-holes 
formed  by  an  oval  punch,  reducing  the  cross-section  of  belt  the  least, 
and  the  lacing  put  in  evenly,  of  equal  strength  at  the  edges  of  the 
belt,  and  no  crossing  of  laces  on  the  inside.  If  copper  or  other  rivets 
are  used,  the  heads  should  be  "  let  in  "  rather  below  the  level  of  the 
inside  surface  of  the  belt  to  prevent  contact  with  the  pulley,  and  the 
washers  placed  on  the  outside  surface.  If  the  bevelled  and  lapped 
ends  are  sewed,  the  waxed  ends  should  be  "  laid  in  "  flush  on  the 
inside  of  the  belt  to  prevent  wear. 

Belts  and  pulleys  should  be  kept  clean  and  free  from  accumulations 
of  dust  and  grease,  and  particularly  from  contact  of  lubricating  oils, 
some  of  which  permanently  injure  the  leather. 

Quick  motion  belts  should  be  made  as  straight  and  as  uniform  in 
section  and  density  as  possible,  and  endless  if  practicable,  that  is, 
with  permanent  joints. 

Horizontal,  inclined,  and  long  belts  give  a  much  better  effect  than 
vertical  and  short  ones  and  those  which  have  the  driving  side  below 
than  otherwise. 

Belts  which  run  loose  of  course  will  last  much  longer  than  those 
which  must  be  drawn  tightly  to  drive,  tightness  being  evidence  of 
overwork  and  disproportion. 


RULES    FOR    BELTING.  47 

Tighteners  should  never  be  used;  but  when  they  must  be,  they 
should  always  be  as  large  in  diameter,  and  as  free  running  as  can 
be,  and  should  be  applied  to  the  slack  side  of  belts. 

The  most  effective  tightener  is  the  weight  of  the  belt  on  its  slack 
side,  which  increases  adhesion  by  increasing  circumferential  contact 
with  the  pulleys. 

"  Belts  which  run  perpendicularly  should  be  kept  tightly  strained, 
and  should  be  of  well-stretched  leather,  as  their  weight  tends  to  de- 
crease their  close  contact  with  the  lower  pulley." — J.  B.  Hoyt  &  Co. 

"  Belts  of  coarse,  loose  leather  will  do  better  service  in  dry,  warm 
places ;  for  wet  or  moist  situations  the  finest  and  firmest  leather  should 
be  used."  —  /.  B.  Hoyt  &  Co. 

"  Care  should  be  taken  that  belts  are  kept  soft  and  pliable.  The 
question  is  often  asked :  '  What  is  best  for  this  purpose  ? '  We  advise, 
when  the  belt  is  pliable,  and  only  dry  and  husky,  the  application 
of  blood-warm  tallow ;  this  applied,  and  dried  in  by  heat  of  fire  or 
sun,  will  tend  to  keep  the  leather  in  good  working  condition ;  the 
oil  of  the  tallow  passes  into  the  fibre  of  the  leather,  serving  to  soften 
it,  and  the  stearine  is  left  on  the  outside  to  fill  the  pores  and  leave  a 
smooth  surface." 

"  The  addition  of  resin  to  the  tallow  for  belts  used  in  wet  or  damp 
places,  will  be  of  service  and  help  preserve  their  strength.  Belts 
which  have  become  hard  and  dry  should  have  an  application  of 
neat's-foot  or  liver  oil,  mixed  with  a  small  quantity  of  resin ;  this 
prevents  the  oil  from  injuring  the  belt  and  helps  to  preserve  it. 
There  should  not  be  so  much  resin  as  to  leave  the  belt  sticky." — 
J.  B.  Hoyt  &  Co. 

Eel-skin  Bands  and  Ropes. 

39.  "  I  have  used  eel-skin  upwards  of  twenty  years,  for  drilling 
holes  for  pearls  and  diamonds,  by  which  means  I  have  a  knowledge 
of  its  utility.  I  have  tried  whip-cord,  which  will  not  last  an  hour ; 
I  have  tried  also  cat-gut,  and  that  indeed  is  very  little  better.  An 
eel-skin  cut  in  three  or  four  pieces  of  the  same  size  as  the  gut,  or 
string,  will  last  for  three  or  four  months  certain,  which  shows  the 
little  wear  to  which  it  is  subject.  I  have  had  them  on  the  shelf  for 
from  six  to  twelve  months,  in  the  dusty  shop,  till  they  have  been 
quite  hard,  yet  they  are  as  good  as  ever.  .  .  .  My  business  is 
that  of  a  goldsmith  and  jeweller."  —  Joseph  Williams,  England, 
"  Journal  Franklin  Inst."  April,  1844. 


48  RULES    FOR    BELTING. 

Driving  Power  of  Belts. 

40.  "  As  regards  the  width  of  the  belt,  this  will  be  found  ample 
with  respect  to  friction,  if  we  calculate  the  cross-section  of  the  same 
for  the  strain  to  be  transmitted,  in  which  case  |  of  an  inch  square  is 
allowed  for  every  5  Ibs.  strain."  —  C.  D.  Abel,  in  Weale's  Series. 

"Morin  concludes  that  we  may,  without  any  risk,  and  with  the 
certainty  that  they  will  run  a  long  time,  make  them  support  tensions 
of  355  Ibs.  per  square  inch  of  section."  —  Frank.  Inst.  Jour.,  July, 
1844,  p.  27. 

"  Good  belting  of,  say,  T3g  inch  thick,  should  sustain  a  tensional 
strain  of  50  Ibs.  per  inch  of  width,  and  without  serious  wear,  for  a 
long  time."  —  Appleton's  Mech.  Mag. 

Haswell,  in  his  Engineer's  Pocket-book  for  1867,  says:  "A  leather 
belt  will  safely  and  continuously  resist  a  strain  of  350  Ibs.  per  square 
inch  of  section." 

We  are  indebted  to  Prof.  R.  H.  Thurston,  for  the  following  : 

7000  x  HP 


In  which  w  =  width  of  belt  in  inches. 

HP  =  indicated  horse-power  transmitted. 

S  =  portion  of  circumference  of  smaller  pulley  covered  by 

belt,  in  feet. 
V=  velocity  of  belt,  in  feet,  per  minute. 

Prof.  Thurston  considers  100  Ibs.  per  inch  of  width  on  ordinary 
belting  of,  say,  -f$  inch  thick,  a  fair  working  load.  Then  calling 
t  =  tension,  and  inserting  same  in  the  formula  above,  we  have  : 

700,000  HP 


Cone  Pulleys.     (From  "Rankine's  Rules  and  Tables.") 

41.  "  To  find  the  ratio  of  the  speed  of  turning  of  two  pulleys  con- 
nected by  a  band.  Measure  the  effective  radii  of  the  pulleys  from 
the  axis  of  each  to  the  centre  line  of  the  band  ;  then  the  speeds  of 
turning  will  be  inversely  as  the  radii. 

"  To  design  a  pair  of  tapering  speed-cones,  so  that  the  belt  may  fit 
equally  tight  in  all  positions. 

"  When  the  belt  is  crossed,  use  a  pair  of  equal  and  similar  cones 
tapering  opposite  ways. 


RULES    FOB    BELTING.  49 

"  When  the  belt  is  uncrossed,  use  a  pair  of  equal  and  similar  con- 
oids tapering  opposite  ways,  and  bulging  in  the  middle,  according  to 
the  following  formula :  Let  c  denote  the  distance  between  the  axes 
of  the  conoids ;  rt  the  radius  of  the  larger  end  of  each ;  r2  the  radius  of 
the  smaller  end ;  then  the  radius  in  the  middle,  r0,  is  found  as  follows : 

__  ry  +  r,,        (r,  —  r,)« 
°  2  6.28c 


"  Line  upon  Line,  here  a  Little  and  there  a  Little." 

4%.  Experience  says,  the  grain  side  of  a  belt  put  next  to  the 
pulley  will  drive  34  per  cent,  more  than  the  flesh  side. 

"  Every  one  knows  that  the  strength  of  belt  leather  is  on  the  hair 
side."  To  be  convinced  of  the  contrary,  see  Article  No.  49. 

If  variation  of  speed  has  resulted  from  changing  belts,  then  the 
thickness  of  the  belt  is  the  cause.  Some  engineers  add  the  thickness 
of  the  belt  to  the  diameter  of  the  pulley  in  their  calculations  for 
exact  transmission  of  speed. 

It  is  not  adhesion  alone  we  want  to  prove  the  better  belt ;  beyond 
a  certain  amount  it  is  rather  an  injury  to  the  belt  than  an  advantage 
in  its  use ;  for  slippage  is  to  be  preferred  to  abrasion,  when  rapid 
destruction  of  the  belt  would  result  from  the  closeness  of  its  sticking. 

Put  the  horse-power  above  and  the  speed  of  the  belt  in  hundreds 
of  Fpm  below,  draw  a  line  between  and  you  have  a  fraction  whose 
equivalent  is  the  width  of  the  belt  in  feet.  To  make  this  rule  ap- 
parent, consider  the  following  example,  in  which  36  horse-power  is  to 
be  transmitted  by  a  belt  moving  1800  Fpm ;  how  wide  should  the 
belt  be? 

36 


Experiments  show  that  a  |  inch  round  belt  is  more  than  equal  to  a 
one  inch  flat,  and  a  ^  inch  round  more  than  a  3  inch  flat,  in  so  far  as 
adhesive  quality  is  concerned.  The  rounds,  of  course,  must  be  used  in 
V- grooved  wheels ;  comparative  durability  will  depend  much  upon 
quality  of  material  and  circumstances  of  use. 

Don't  put  a  crossed  belt  on  so  that  at  the  place  of  passing  the  laps 
will  be  torn  up,  and  joints  severed  in  a  short  time. 
4 


50  RULES    FOR    BELTING. 

Don't  cross  the  lacing  of  a  belt  joint  on  the  inside,  when  there  is  a 
way  to  avoid  crossing  the  lacing  at  all.  See  Article  No.  144. 

Of  course  belts  are  weakened  by  punching  for  laces  or  rivets  just 
in  proportion  to  the  amount  cut  out ;  it  is  therefore  necessary  to  nar- 
row the  punch,  say  to  an  oval  form,  to  reduce  the  number  of  holes 
to  the  least,  or  to  range  them  fore  and  aft,  preserving  the  most  sub- 
stance in  any  straight  line  across  the  belt. 

Experiments  have  shown  that  f  of  the  breaking  strain  of  the  solid 
part  will  start  rupture  at  the  lace  holes  in  leather  belts,  and  that 
they  will  endure  ^  of  the  breaking  strain  for  a  week  without  appear- 
ance of  fracture. 

We  thank  a  correspondent  kindly  for  having  exercised  his  inge- 
nuity upon  methods  of  strengthening  lace  holes,  especially  in  gum 
belts,  and  after  much  experimenting  has  generously  presented  to  us 
this  result :  "  With  large  oval  eyelets,  securely  put  in,  the  breaking 
strength  of  the  joint  was  nearly  up  to  that  of  the  solid  section." 

__  velocity  in  Fpm  X  width 
1000 


Driving  value  of  double  belts  as  compared  with  single  leather, 
10  to  7. 


Leather  belts  should  not  be  forced  over  ygth,  and  rubber  belts  not 
over  |th  of  their  breaking  strength. 

"All  belts  riveted  to  run  with  the  grain  side  next  pulley.  They 
will  do  one-third  more  work  than  with  flesh  side  to  pulley  —  will  last 
longer,  and  will  never  crack."  —  English  Advertisement. 

Thoroughly  stretched  belting  leather  is  more  liable  to  tearing  at 
the  lace  holes  under  undue  strains,  because  less  elastic  ;  but  it  must 
not  be  condemned  on  that  account.  A  belt  poorly  stretched  will 
yield  too  readily  to  strains,  and  will  require  re-tightening  often. 

Rule  for  Piecing  out  Belts. 

43.  In  order  to  calculate  the  changed  length  of  belt  when  a 
different  size  pulley  is  put  on  in  place  of  one  removed,  take  out  of 
the  belt  or  put  in  1J  times  the  difference  of  the  diameters  of  the 
pulleys. 

Thus  :  If  you  take  off  a  24-inch  pulley  and  put  on  a  30-inch  one, 
you  will  want  to  add  30  —  24  x  1|  =  9  inches  of  new  belt  to  the 
existing  one. 


RULES    FOR    BELTING.  51 

This  rule  provides  simply  for  the  approximate  difference  of  semi- 
circumferences  of  the  two  pulleys  thus : 

The  dr.  of  30  =  94.24 
The  dr.  of  24  =  75.39 
2)18.85 
9.425 
Example. 

44.  In  hoisting  the  materials  for  the  towers  of  the  Cincinnati 
bridge,  Mr.  John  A.  Roebling,  C.  E.,  used  engines  of  10  inches  bore 
and  20  inches  stroke,  making  80  to  150  Rpm,  and  working  under  a 
steam  pressure  ranging  from  60  to  80  pounds. 

The  power  of  these  engines  is  transmitted  by  a  9-inch  leather  belt, 
from  a  4-feet  iron  pulley  on  the  engine  shaft,  to  another  4-feet  pulley 
on  the  pinion  shaft.  This  pinion  is  14J  inches  diameter,  and  drives 
a  6-feet  spur-wheel :  on  the  shaft  of  this  latter  is  another  14-^  inch 
pinion,  gearing  into  another  6-feet  spur-wheel,  on  the  shaft  of  which 
is  secured  a  3-feet  drum.  This  drum  carries  a  1 J  inch  diameter  wire 
rope,  connected  directly  to  the  loads  to  be  lifted. 

A  block  weighing  8400  pounds  can  be  raised  at  the  rate  of  50  feet 
per  minute  by  pressing  the  tightener  down  so  that  the  belt  laps  on 
-fths  of  the  circumference  of  the  4-feet  pulleys. 

With  a  load  of  10,200  pounds  the  belt  slips,  and  its  splicings  and 
safety  are  endangered  by  too  severe  an  application  of  the  tightener 
which  is  necessary  to  lift  this  weight.  A  load  of  8000  pounds  may 
therefore  be  considered  a  fair  working  condition  of  the  belt,  which 
indeed  it  has  endured  nearly  three  seasons  without  failing. 

Blocks  weighing  8000  pounds  have  been  frequently  raised  150  feet 
high  in  two  and  a  half  minutes  without  slippage  of  the  belt.  This 
speed  is  equal  to  60  Fpm,  and  the  duty  performed  is  equivalent  to 
60  X  8000  =  480,000  Ibs.  =  14.54  horse-power,  speed  of  belt  being 
1885  Fpm. 

Quantity  of  belt  running  per  minute,  per  horse-power  =  97.232 
square  feet. 

Combined  Strap-Shifter  and  Stop -Motion. 

45.  In  the  use  of  sewing-machines  it  is  as  necessary  to  stop  them 
instantly  as  to  drive  them  rapidly,  particularly  for  manufacturing 
purposes,  where  a  speed  of  some  6000  stitches  per  minute  is  made, 
and  where  the  machines   are   repeatedly  started   and   stopped   for 
changing  the  direction  of  the  seam  as  well  as  the  pieces  to  be  sewn. 


52 


RULES    FOB,    BELTING. 


Fig.  7  illustrates  a  little  device  which  answers  this  purpose  so  well 
that  it  deserves  a  record  among  the  good  things  employed  in  the  best 
use  of  belting. 

The  shifting-bar,  A,  guided  by  the  staples,  B  and  C,  secured  to  the 
table,  K,  has  a  notch  in  its  side  for  embracing  the  round  belt,  G, 
which  drives  the  machine,  and  carries  a  brake,  H,  of  leather,  secured 
by  an  adjustable  screw,  to  the  bar,  and  in  such  position  that  when  the 


Fig.  7. 

cord  is  on  the  loose  pulley,  J,  as  shown,  the  brake  is  held  firmly 
against  the  tight  pulley,  I,  by  the  spring,  D,  which  is  always  in 
action. 

To  start  the  machine,  the  foot  of  the  operator  is  pressed  upon  a 
hinged  treadle,  which  is  secured  to  the  floor,  and  attached  by  a  cord, 
"E,  to  the  shifting-bar,  the  direction  of  its  motion  being  changed  by  a 
pulley,  F,  also  fixed  in  the  table,  K.  This  action  draws  the  brake, 
H,  from,  and  puts  the  belt  on,  the  tight  pulley,  I,  at  the  same  time 
distending  the  spring,  D.  When  the  foot  is  lifted,  the  recoil  of  the 
spring  pulls  the  belt  over  on  the  loose  pulley  and  holds  the  brake 


RULES    FOB    BELTING.  53 

against  the  tight  pulley,  instantly  stopping  the  machine  and  holding 
it  still,  without  attention  or  effort  of  the  operator,  until  motion  is 
needed  again,  which  the  simple  act  of  pressing  the  foot  produces  at 

will. 

Atmospheric  Influence  on  Adhesion. 

46.  The  adhesion  of  belts  to  pulleys  is  frequently  attributed  to 
the  pressure  of  the  atmosphere,  and  in  order  to  show  how  much  the 
air  influences  belts  in  this  particular,  the  following  simple  experi- 
ments are  presented. 

Take  a  circular  disc  of  leather,  say  3  or  4  inches  diameter,  with 
knotted  string  secured  in  its  centre,  and,  when  well  water-soaked, 
press  it  upon  any  level  wetted  surface.  The  "  boys  "  call  this  appa- 
ratus a  "  sucker,"  and  it  well  illustrates  the  phenomenon  of  atmos- 
pheric pressure,  or  "  suction,"  as  it  is  usually  called. 

If  an  effort  be  made  to  draw  it  away  from  this  surface  by  the  string, 
it  will  be  found  resisting  very  forcibly,  but  the  gentlest  pressure  will 
slide  it  on  the  wetted  surface ;  it  does  not  offer  the  slightest  opposi- 
tion to  motion  in  the  direction  of  its  face,  nor  will  it  resist  removal  if 
raised  first  at  the  edge  and  then  peeled  off. 

The  atmosphere  does  not  press  two  bodies  together  when  it  can  get 
between  them ;  it  is  only  when  excluded  by  a  tight  joint  that  the 
development  of  its  pressure  is  possible,  and  it  becomes  sensible  only 
when  an  effort  is  made  to  separate  them  by  a  force  acting  at  right 
angles  to  the  plane  of  their  faces. 

Another  simple  experiment  shows  that  when  two  level,  smooth,  and 
clean  surfaces  come  together  by  a  motion  like  the  closing  of  a  book — 
which  is  similar  to  that  of  a  belt  coming  in  contact  with  its  pulley  — 
there  will  be  retained  between  the  two  a  thin  film  of  air,  and,  while  this 
remains,  the  contact  of  the  two  is  imperfect,  and  the  sliding  of  one  over 
the  other  is  easily  performed.  Take  two  iron  "  surface-plates  "  which 
have  been  scraped  down  to  a  practically  perfect  plane,  and  lay  one  of 
these  on  the  other  like  a  belt  goes  to  a  pulley ;  they  will  be  found  not 
in  contact  at  all,  but  as  if  floating  one  on  the  other,  and  the  top  one 
will  slide  off  by  its  own  weight  at  the  least  inclination  of  the  lower  one. 

Much  of  this  interposed  film  of  air  can  be  displaced  by  a  sliding 
of  one  plate  on  the  other,  starting,  say  at  one  corner,  with  the  plates 
in  close  contact,  and  carefully  pushing  one  over  the  other,  holding  it 
the  while  close  to,  as  if  to  keep  the  air  out.  Then,  indeed,  an  obsti- 
nate resistance  to  sliding  will  be  felt,  and  the  friction  of  nearer  con- 
tact will  be  made  thoroughly  sensible. 

But  this  way  of  bringing  surfaces  into  contact  has  nothing  to  do 


54  RULES    FOB    BELTING. 

with  belt  action,  except  to  prove  the  need  of  a  plastic  surface  on  belt 
and  pulley  which  will  enable  them  to  adhere,  while  in  contact,  with 
sufficient  force  to  prevent  sliding,  and  at  the  same  time  be  uninflu- 
enced by  the  intermedium  of  air. 

And  lastly,  in  order  to  put  the  matter  to  actual  test,  an  apparatus 
was  constructed,  such  that  a  leather  belt  was  made  to  slide  on  the 
face  of  a  smooth  iron  pulley,  and  also  to  drive  the  same  iron  pulley 
up  to  slipping  of  the  belt.  In  both  cases  the  adhesion  or  driving 
power  of  the  belt  was  held  by  a  spring-balance,  so  that  the  work  of 
the  belt  could  be  observed. 

Experiments  were  tried  with  this  mechanism  placed  in  a  bell-glass 
jar  on  an  air-pump  plate,  with  and  without  air  in  the  jar,  and  if  any 
difference  was  observed  in  the  adhesion  of  the  belt  to  the  pulley,  it 
had  more  in  vacuum  than  when  the  atmosphere  was  present. 

Messrs.  J.  B.  Hoyt  &  Co.  kindly  permit  me  to  reproduce  their 
valuable  practical  statements  and  experiments. 

47.  "  Good  leather  belts  can  only  be  obtained  by  employing  good 
materials.  We  stretch  every  piece  by  powerful  machinery,  joint  it 
and  secure  it  in  such  a  manner  as  that  both  sides  will  present  an 
even  surface  to  the  pulley,  and  run  on  it  as  though  it  were  one  strip. 
The  fact  that  there  is  a  great  want  of  information  in  relation  to  the 
selection  and  use  of  belting  must  be  apparent  to  all  who  have  given 
thought  to  the  subject.  While  the  '  what,  how,  and  why '  of  every 
other  subject  connected  with  machinery  seems  to  have  been  exten- 
sively considered,  that  of  belting  has  been  almost  entirely  passed  over. 

"  We  have  inserted  a  useful  table,  with  calculations  and  deductions 
from  it.  These  we  believe  to  be  correct,  the  experiments  having 
been  made  at  our  factory. 

"  This  table  gives  the  relative  driving  power  of  leather  belting, 
with  both  grain  and  flesh  side  to  pulley ;  also,  of  rubber,  gutta- 
percha,  and  canvas.  The  pulleys  on  which  the  experiments  were 
made  were  the  same  in  size,  on  one  shaft,  and  their  surfaces  sev- 
erally of  leather,  polished  iron,  rough-turned  iron,  and  of  polished 
mahogany.  The  bands  were  passed  over  the  pulley,  one  end  made  fast 
and  stationary,  and  on  the  other  one  pound  weight  was  suspended  to 
every  square  inch  contact  surface  of  the  band  and  pulley. 

"  The  number  of  pounds  required  to  slip  the  band  is  given ;  also, 
number  of  pounds  strain  on  the  band  at  which  it  will  cease  to  slip ; 
and  also,  number  of  pounds  required  to  make  it  continue  to  slide. 

"  The  belts  were  in  like  condition,  and  had  the  same  contact  sur- 


RULES    FOR    BELTING. 


55 


face,  the  same  strain  ;  consequently  it  is  easy  to  determine  the  relative 
value  of  each  for  driving  machinery,  also  that  of  the  pulleys. 


LEATHER. 
Grain  side 
to  Pulley. 

LEATHER. 
Flesh  side 
to  Pulley. 

RUBBER. 

GUTTA- 
PERCHA. 

CANVAS. 

-2     | 

3 

3 

3 

o 

s^ 

3H 

-r-r 

8 

3 

8 

3 

4> 

s 

a> 

s 

*    S    (C 

0)    Q, 

Tl 

Sjf 

g* 

§.& 

a! 

JS 

fl  d 
§.§ 

ga 

S 

^1^" 

s~n 

fi-3 

-  M 

Q    02 

7r) 

c  02 

to    OQ 

^ 

S  a: 

o3  ^ 

~ 

S  '^ 

*n  S  ^ 

A 

O 

s 

O 

^ 

Q^ 

§ 

^) 

c3         ^H 

8 

a 

O 

O 

p 

3° 

Pulley  with  Lea- 
ther surface  

6 

8X 

10 

8X 

2K 

7 

2* 

1U 

6 

2X 

iK 

8X 

1% 

1 

134 

52 

Polished       Iron 

IX 

1 

9 

IK 

% 

6X 

jix 

% 

4X 

^ 

X 

2X 

1 

X 

2 

33% 

Rough  Iron  sur- 

face   
Smooth     turned 

IX 

% 

3 

IX 

% 

2K 

jix 

% 

4 

% 

X 

IX 

i 

% 

IK 

21X 

Mahogany  

3% 

2K 

4 

3 

IX 

3K 

2K 

IX 

4X 

2X 

1 

2X 

1% 

IK 

1% 

36% 

Relative  value  of 

each  belt  

45% 

MX 

29% 

19% 

15% 

*  "Commencing  to  slip"  refers  to  that  point  when  the  resistance  is  sufficient  to  make  the 
belt  (almost,  not  quite)  slip  over  the  pulley. 

f  "Cease  to  slip"  refers  to  that  point  when  the  belt  has  just  slipped  over  the  pulley  and 
takes  a  new  hold. 

J  "  Slide "  refers  to  that  condition  when  the  motion  of  either  belt  or  pulley  ceases  while 
the  other  passes  over  it. 

>8®^  Belts  are  liable  to  stretch  more  or  less,  decreasing  their  tension,  so  that  they  will  slip  — 
hence  the  necessity  for  the  above  distinction. 

Deductions  and  Conclusions  drawn  from  Table. 

"  Pulleys  covered  with  leather,  with  grain  side  of  band  to  pulley, 
will  sustain  50  per  cent,  more  resistance  than  without  the  pulley  being 
covered.  The  per  cent,  of  resistance  of  the  bands  on  the  different 
pulleys  is  nearly  as  follows,  and  this  per  cent,  will  indicate  the  rela- 
tive working  value  of  each  pulley  respectively : 

Iron  pulley  covered  with  leather 36  per  cent. 

polished 24 

rough  turned 15        " 

Wood  pulley,  polished  mahogany 25       " 

loo 

"  Full  6  per  cent,  should  be  added  to  the  polished  iron  pulley,  to 
make  allowance  for  the  difference  between  commencing  to  slip  and  its 
sliding ;  thus  making  polished  pulley  30  per  cent.,  or  next  in  value 
to  leather. 

"  The  relative  or  comparative  working  per  cent,  of  the  different 
bands,  as  indicated  by  the  table,  is  nearly  as  follows : 


56  RULES    FOB    BELTING. 

Leather,  grain  side  to  pulley 31  percent. 

flesh     "        "  23 

Rubber 21       « 

Gutta-Percha 14 

Canvas 11       " 

100 

"  Thus  leather  belts,  grain  side  to  pulley,  will  drive  34  per  cent, 
more  than  flesh  side  to  pulley  ;  48  per  cent,  more  than  rubber ;  121 
per  cent,  more  than  gutta-percha ;  180  per  cent,  more  than  canvas  ; 
consequently,  the  very  best  arrangement  for  belting  is  to  use  it  with 
grain  side  to  pulley,  and  have  the  pulley  covered  with  leather. .  This 
is  best  in  all  cases.  The  next  best  pulley  is  polished  iron,  especially 
for  quick  motions ;  polished  wood  next,  and  rough  iron  least  in  value. 

"  Leather,  used  with  grain  side  to  pulley,  will  not  only  do  more 
work,  but  last  longer  than  if  used  with  flesh  to  same.  The  fibre  of 
the  grain  side  is  more  compact  and  fixed  than  that  of  the  flesh,  and 
more  of  its  surface  is  constantly  brought  in  contact,  or  impinges  on 
the  particles  of  the  pulley.  The  two  surfaces  —  that  of  the  band  and 
that  of  the  pulley  —  should  be  made  as  smooth  as  possible ,  the  more 
so  the  greater  the  contact  surfaces,  and  the  more  the  particles  of  each 
impinge  on  the  other.  The  smoother  the  two  surfaces,  the  less  air 
will  pass  under  the  band  and  between  it  and  the  pulley  —  the  air 
preventing  the  contact  of  band  with  pulley  —  the  greater  this  contact, 
the  more  machinery  will  the  band  drive.  The  more  uneven  the  sur- 
face of  band  and  pulley,  the  more  strain  will  be  necessary  to  prevent 
bands  from  slipping.  What  is  lost  by  want  of  contact  must  be  made 
up  by  extra  strain  on  the  band,  in  order  to .  make  it  drive  the  ma- 
chinery required  —  oftentimes,  if  the  band  is  laced,  causing  the 
lacings  to  break,  the  holes  to  tear  out,  or  fastenings  of  whatever 
kinds  to  give  way. 

"  This  want  of  contact  is  noticeable  on  most  of  new  bands  used  with 
flesh  side  to  pulley,  and  is  distinctly  marked  by  dark  impressions  on 
the  baud  where  it  comes  in  contact  with  the  pulley.  Oftentimes  not 
half  of  the  surface  will  be  found  to  have  come  in  contact,  and,  until 
it  is  worn  smooth,  or  filled  in  with  other  substances,  the  full  extent 
of  the  power  of  the  baud  is  not  obtained.  .  .  . 

'*  Bands  used  with  grain  side  to  the  pulley  will  never  crack  ;  as  the 
strain,  in  passing  it,  is  thrown  on  the  flesh  side,  which  is  not  liable  to 
crack  or  break,  the  grain  not  being  strained  any  more  than  other 
portions  of  the  band. 


RULES    FOR    BELTING.  57 

Rule  for  determining  the  Width  of  Belts. 

48.  5884  HP 

V  C 

In  which   W=  width  of  belt  in  inches. 
HP=  horse-power  transmitted. 
"  V=  velocity  of  belt  per  minute  in  feet. 

C=part  of  circumference  of  smaller  pulley  in  contact 
with  belt  in  feet. 

We  take  pleasure  in  presenting  the  following  facts  contributed 
by  Alexander  Brothers,  manufacturers  of  Oak-Tanned  Leather 
Belting,  Philadelphia. 

49.  "  It  is  conceded  by  all  practical  men,  that  oak-tanned  slaughter 
leather  is  the  best  material  for  belting,  and  as  inferior  stock  such  as 
chemical  tanned  and  hemlock  leather,  colored  in  imitation  of  oak,  by 
means  of  quercitron,  sumac,  etc.,  is  largely  used  in  the  manufacture 
of  belting,  purchasers  should  be  cautious,  in  buying,  not  to  get  any 
but  pure  oak-tanned  leather. 

"  The  strongest  part  of  belt  leather  is  near  the  flesh  side,  about 
one-third  the  way  through  from  that  side.  It  is,  therefore,  desirable 
to  run  the  grain  side  on  the  pulley,  in  order  that  the  strongest  part 
of  the  belt  may  be  subject  to  the  least  wear. 

"  In  order  to  prove  the  above  assertion,  we  split,  in  our  machine, 
a  strip  of  ordinary  belt  leather  exactly  in  the  middle  of  its  thickness, 
and  then  subjected  each  half  to  a  breaking  tension,  which  gave  the 
following  results:  —  Grain  side  half  broke  under  a  direct  strain  of 
468^  Ibs.  Flesh  side  half  sustained  740J  Ibs. 

"  A  part  of  the  grain  side  half  is  of  the  same  kind  of  fibre  as  that 
of  the  flesh  side,  and  as  the  grain  extends  but  about  one-fourth 
the  way  through  a  hide,  much  of  the  strength  of  the  grain  half  in 
this  experiment  is  due  to  the  flesh  part  adhering  to  it. 

"  The  flesh  side  is  not  liable  to  crack,  as  the  grain  sometimes  will 
do  when  the  belt  is  old,  hence  it  is  better  to  crimp  the  grain  than  to 
stretch  it. 

"Another  important  reason  for  running  belting  with  the  grain  side 
on  the  pulley,  is  to  get  greater  driving  power ;  that  being  the  smooth- 
est side,  it  will  hug  closer,  is  less  liable  to  slip,  and  will  drive  30  to 
35  per  cent,  more  than  if  run  the  other  way ;  and  if  the  pulley  is 
covered  with  leather,  grain  side  out,  there  will  be  still  greater  fric- 


58  RULES    FOR    BELTING. 

tion.  Therefore  a  belt  will  do  more  work  and  wear  longer  on  a 
leather-covered  pulley  than  on  any  other. 

"  Belts  should  not  be  soaked  in  water  before  oiling,  and  penetrating 
oils  should  but  seldom  be  used,  except  occasionally  when  a  belt  gets 
very  dry  and  husky  from  neglect,  it  may  be  moistened  a  little  and 
then  have  straits  or  neat's-foot  oil  applied.  Frequent  applications 
of  such  oils  to  a  new  belt  renders  the  leather  soft  and  flabby,  thus 
causing  it  to  stretch  and  making  it  liable  to  run  out  of  line.  A  com- 
position of  tallow  and  oil,  with  a  little  resin  or  beeswax,  is  better  to 
use.  Whitaker's  castor-oil  dressing  is  good,  and  may  be  applied  with 
a  brush  or  rag  while  the  belt  is  running." 

"  We  find  the  average  permanent  stretch  of  oak-tanned  leather  for 
belting  to  be  about  .725  in.  per  lineal  foot,  or  as  follows : 

"  Average  stretch  of  back  pieces  per  foot,  .562  inch, 
middle  cuts      "  .75     " 

lower  edge        "          .875    "     " 

Cones  of  Pulleys. 

50.  When  2  cones  of  pulleys,  or  "stepped  cones,"  are  made 
alike,  i.  e.t  with  equal  steps,  such  that  the  sum  of  the  diameters  of 
each  belted  pair  is  the  same,  a  crossed  belt  will  run  with  equal  tension 
on  any  pair  so  made,  when  the  shafts  are  parallel  and  the  cones 
reversed ;  but  an  uncrossed  belt  will  not  so  run  on  such  cones. 

To  show  why  the  open  belt  will  not  have  equal  tension  on  all  the 
pulleys,  let  A  B,  Fig.  8,  be  two  equal  stepped  cones  on  parallel  axes 
A  E  and  B  D.  Now,  if  the  sum  of  the  diameters  of  the  extreme 
pulleys  E  and  F  be  equal  to  the  sum  of  the  diameters  of  C  and  D, 
the  connecting  strips  E  F  and  C  D  of  the  belt  will  be  equal,  because 
the  enrolled  parts  are  equal  by  the  construction  of  the  cones ;  but  E 
F  and  C  D  cannot  be  equal,  because  they  are  not  parallel,  and  hence 
it  plainly  appears  that  C  D,  being  at  right  angles  to  the  shafts,  is 
shorter  than  E  F ;  therefore,  to  preserve  a  certain  tension  of  the  belt 
when  on  the  extreme  pulleys,  the  middle  pulleys  must  be  larger  than 
the  size  given  by  equal  steps  in  order  to  take  up  this  difference. 

To  find  the  proper  diameters  of  the  intermediate  pulleys  for  open 
belt  cones,  first  get,  by  Rankine's  rule,  Art.  41,  the  radius  N  O  from 
the  given  radii  I  J,  K  L,  and  distance  between  shafts  and  through 
the  points  J  O  L  describe  a  circular  arc,  upon  which  draw  the  faces 
of  all  the  pulleys  in  the  series  as  shown.  Make  both  cones  by  this 
rule,  and  an  open  belt  will  run  upon  them  with  equal  tension. 

Unequal  cones  may  be  made  in  like  manner  by  drawing  2  similar 


RULES    FOR    BELTING. 


59 


cones,  and  then  using,  say  S  T  V  of  the  large  end  of  one,  and  X  Y  Z 
of  the  small  end  of  the  other,  as  needed  to  serve  the  purpose. 


Fig.  8. 

For  wheels  driven  by  round  bands  in  V  grooves  the  same  rules 
apply,  observing  that  the  effective  diameters  must  be  taken  at  the  line 
of  band  contact  in  the  grooves,  which  are  the  acting  circles  of  adhe- 
sion. All  the  grooves  must  be  alike,  and  should  have  concave  instead 
of  straight  sides,  like  a  Gothic  arch,  and  the  band  must  not  touch 
the  bottom  of  the  groove. 

Belts. 

51.  "The  effective  radius  of  a  pulley  is  equal  to  the  radius  of 
the  pulley  added  to  one-half  the  thickness  of  the  belt. 

"  In  ordinary  cases  a  belt  will  last  about  three  years. 

"  Leather  belts  must  be  well  protected  against  water,  and  even 
moisture. 

"  India  rubber  is  the  proper  substance  for  belts  exposed  to  the 
weather,  as  it  does  not  absorb  moisture  and  stretch  and  decay. 

"  It  is  quite  probable  that  these  belts  will  increase  in  popularity 
among  manufacturers. 

"  In  joining  the  ends  of  a  belt,  it  is  generally  considered  best  to 
cut  small  holes  through  the  ends  and  lace  them  with  a  leather  strap. 

"  It  is  found,  in  practice,  that  belts  should  not  be  subjected  to  a 
strain  of  over  300  pounds  per  square  inch  of  section. 

"  Good  belting  of  T3^  inch  thick  will  sustain  a  strain  of  50  pounds 
per  inch  width  without  risk,  and  without  serious  wear,  for  a  considera- 
ble time." —  Amer.  Artisan,  July  1,  '68,  p. 


60  KTJLES    FOR    BELTING. 

Belts  and  Pulleys. 

52.  "  We  would  not  venture  to  prophesy  that  belts  will  continue 
for  ever  in  general  use,  especially  if  made  of  leather,  in  the  old  way. 
Nor  is  our  faith  in  the  perpetuity  of  small  pulleys  very  resolute. 
Robertson's  frictional  gearing  seems  to  work  more  steadily  than  belts; 
but  if  pulleys  are  large,  the  friction  of  their  faces  against  each  other 
is  sufficient  for  most  work,  and  they  will  run  with  less  power  than 
belts  or  Robertson's  gearing.  To  make  pulleys  work  well  against 
each  other,  they  must  be  turned  with  more  truth  than  is  usual ;  and 
the  shafting  must  be  better  lined ;  and  there  must  be  something  elastic 
in  the  journal-boxes,  such  as  a  little  rubber,  to  press  the  pulleys  to- 
gether. 

"The  vibration  or  chattering  of  lathes  is  probably  due  to  the 
spring  of  the  belts,  more  than  to  the  spring  of  the  metal  of  the 
lathes.  So  far  as  this  is  the  case,  the  frictional  gearing,  of  either 
kind,  will  get  rid  of  it. 

"  In  driving  fans  there  is  frequent  trouble  with  belts,  and  there  is 
more  expense  than  need  be;  and  the  noise  and  vibration  are  evi- 
dences of  serious  imperfection,  which,  perhaps,  is  unavoidable  when 
a  soft  material  is  used  that  cannot  have  an  exact  shape. 

"  A  friend  of  ours  proposes  to  use  steel  belts  for  certain  cases,  such 
as  fans.  The  steel  must  be  welded  perfectly,  and  must  be  of  mild 
quality,  and  the  pulleys  must  be  large,  to  make  them  work  well. 
Steel  belts  would  run  with  less  power  than  leather,  because  the  power 
exerted  in  bending  them  would  be  restored  when  they  straightened 
themselves ;  but  leather  does  not  return  much  of  the  power  required 
to  bend  it  around  the  pulley.  .  .  ." — Amer.  Artisan,  Aug.  2,  '65 f 
p.  201. 

Leather  Belts. 

S3»  "A  friend  of  ours  who  has  had  experience  in  tanning  leather 
for  belts,  and  has  conversed  about  belts  with  many  machinists,  and 
is  familiar  with  their  experience,  assures  us  that  the  adhesion  of  belts 
is  much  better  when  the  hair  side  is  against  the  pulleys,  and  that  the 
belt  used  in  this  way  is  more  durable.  The  belt  will  not  crack  on 
the  flesh  side  so  readily  as  on  the  hair  side,  and  seldom  cracks  at  all, 
if  the  hair  side  is  against  the  pulley.  He  has  known  cases  in  which 
belts  slipped  and  would  not  do  the  work  required  of  them  when  the 
flesh  side  was  against  the  pulley ;  but  when  they  were  turned  hair 
side  to  the  pulleys  they  ceased  to  slip,  and  did  much  more  work  than 
they  could  do  with  the  flesh  side  to  the  pulleys.  His  theory  is,  that 


RULES    FOR    BELTING.  61 

the  belt,  as  well  as  the  pulley,  adheres  best  when  smooth,  and  the 
hair  side  adheres  best  because  it  is  smoothest." — Amer.  Artisan,  Aug. 
16,  '65,  p.  234. 

From  "  Power  in  Motion,"  by  J.  Armour,  C.  E.    Lockwood  &  Co., 

London,  1871. 

54.  "  Good  new  belt  leather  has  been  found  to  break  with  an 
average  tension  of  5000  Ibs.  applied  quietly  per  square  inch  of  sec- 
tional area. 

"  The  working  tension  for  continuous  service  ought  not  to  be  more 
than  about  T\  of  this,  or  about  350  Ibs.  per  square  inch. 

"  A  thickness  of  -f$  of  an  inch,  which  is  the  ordinary  thickness, 
equals  .186  inch  :  therefore,  for  an  inch  of  breadth,  we  have  .186  X 
5000  =  930  Ibs.  breaking  strain,  and  .186  x  350  =  65.1  Ibs.  contin- 
uous service  strain. 

"  With  the  same  working  tension,  when  we  double  the  breadth,  we 
reduce  the  strain  per  square  inch  of  section  to  one-half  the  strain  for 
the  single  breadth,  and  thereby  save  the  belt.  The  axle  pressure  is 
the  same,  however,  because  the  belt  of  double  breadth  is  simply  doing 
the  same  amount  of  work  upon  the  rim  of  the  pulley  as  the  single 
breadth  had  to  perform. 

"When  we  double  the  diameter,  the  revolutions  of  pulley  per 
minute  being  as  before,  we  may  reduce  the  tension  to  one-half;  be- 
cause we  have  the  speed  at  the  circumference  equal  to  2,  and  this 
multiplied  by  .5  tension  =  1  power ;  the  same  as  1  speed  X  1  tension 
=  1  power. 

"  When  two  pulleys  at  rest  are  connected  by  a  belt,  the  tension  on 
each  connecting  part  is  nearly  equal ;  when  motion  begins,  the  driving 
pulley  has  to  stretch  the  pulling  parts  to  the  tension  required  to  over- 
come the  resistance  before  the  driven  or  loaded  pulley  can  move ; 
and,  in  doing  so,  the  driver  is  passing  a  corresponding  amount  of 
slack  into  the  returning  part. 

"Should  the  resistance  of  the  load  grow  less  from  any  cause,  less 
tension  will  be  required  to  balance  it,  and  the  driven  pulley  will  be 
moved  by  the  excess  of  the  pulling  tension  a  fractional  quantity  faster 
than  the  driver,  thereby  throwing  part  of  the  slack  of  the  returning 
part  into  the  pulling  part,  until  the  reduced  load  resistance  and  the 
pulling  tension  come  to  a  balance ;  this  diminishes  the  amount  of 
slack  on  the  returning  part. 

"  On  the  other  hand,  should  the  load  increase  from  any  cause, 
greater  tension  is  required ;  the  driver  must  move  a  fractional  quan- 


62  RULES    FOR    BELTING. 

tity  more  than  the  loaded  pulley,  to  put  the  greater  strain  upon  the 
belt,  and  the  amount  of  slack  is  increased  correspondingly. 

"  Hence,  in  a  narrow  belt  the  returning  part  will  be  slacker  than 
when  a  broader  belt  is  employed,  because  it  will  stretch  more  with  a 
given  tension. 

"  Short  belts  require  to  be  tighter  than  long  ones.  A  long  belt, 
working  horizontally,  increases  the  tension  by  its  own  weight,  acting 
in  the  curve  formed  between  the  pulleys. 

"  One  of  the  properties  of  this  curve  is  to  make  the  tension  greater 
than  is  due  to  the  simple  weight  of  the  belt ;  that  is  greater  than  when 
the  belt  is  hanging  vertically  ;  besides,  it  never  loses  contact. 

"  In  vertical  belts  so  little  stretch  is  needed  to  make  them  lose 
contact  with  the  lower  pulley,  that  the  tension  for  the  state  of  rest 
requires  to  be  greater  than  is  found  necessary  for  a  horizontal  belt, 
if  the  breadth  be  not  increased  to  reduce  the  stretching  stress  per  sec- 
tional square  inch. 

"  In  ordinary  leather  belts,  on  large  pulleys,  the  bending  resistance 
is  so  small  that  it  may  be  disregarded. 

"  Ropes  of  hemp  or  wire  are  often  employed  for  driving  bands. 
Their  resistance  to  bending  is  greater  than  that  of  flat  leather  belts, 
and  as  the  surface  in  contact  with  the  pulling  is  less,  the  pressure  per 
square  inch  of  actual  contact  must  be  greater,  and  therefore  more 
severe  upon  the  material. 

"  This,  however,  does  not  affect  the  amount  of  tension  required  for 
work,  because,  as  friction  is  independent  of  the  extent  of  surface,  we 
get  the  same  driving  power  from  10  Ibs.  pressure  or  tension  on  the 
narrow  line  of  contact  with  the  pulley,  in  the  case  of  a  circular  rope, 
that  we  would  get  from  the  same  pressure  supposing  the  rope  flat- 
tened out  so  as  to  have  a  surface  of  contact  many  times  greater. 

"  When  we  know  the  weight  per  foot  of  a  long  belt  or  rope  work- 
ing horizontally,  we  find  the  tension  in  the  curve  of  the  belt  between 
the  pulleys  by  multiplying  the  whole  weight  of  the  part  between  the 
pulleys  by  the  distance  between  the  same,  and  dividing  by  eight  times 
the  deflection.  This  rule,  however,  applies  only  to  curves  in  which 
the  deflection  is  small  compared  with  the  span  ;  so  that  the  flatter  the 
angle  of  suspension  the  closer  the  approximation." 

I.  H.  Beard  on  Belts. 

55.  "  Throughout  New  England,  until  within  a  few  years,  it  was 
generally  thought,  by  engineers  and  millwrights,  that  cotton-mills  and 
woollen-mills,  and  all  others  requiring  a  very  considerable  power, 


RULES    FOR    BELTING.  63 

could  not  be  run  effectively  without  large  and  ponderous  lines  of 
upright  and  horizontal  shafts  of  either  cast  or  wrought  iron,  and 
heavy  trains  of  cog-wheels  of  cast  iron,  or  partly  of  iron  and  partly 
of  wood. 

"And  when  large  leather  belts  began  to  be  introduced  for  the  main 
gear  of  mills,  as  a  substitute  for  gear-wheels,  it  was  thought  by  some 
of  our  best  engineers  to  be  an  experiment,  at  the  least,  of  very  doubt- 
ful result,  if  not  altogether  impracticable ;  and,  indeed,  at  the  present 
time  (1837),  notwithstanding  all  the  evident  advantages  of  belts  over 
gear-wheels,  many  still  adhere  to  the  old  mode  of  gearing ;  and  this, 
doubtless,  not  so  much  from  a  want  of  discernment  and  sound  judg- 
ment, as  from  a  lack  of  opportunity  of  comparing  and  testing  the 
advantages  of  belts  and  the  disadvantages  of  gear-wheels ;  or,  per- 
haps, they  may  have  formed  an  erroneous  opinion  of  the  utility  of 
using  belts  from  the  inspection  of  some  mills  that  have  been  belted 
on  a  bad  principle,  or  from  belts  injudiciously  managed." 

"  Having,  from  a  constant  practical  experience  of  both  modes  of 
gearing  mills,  for  more  than  ten  years,  at  Lowell,  Saco,  and  other 
places,  become  fully  satisfied  of  the  utility  of  belting  mills,  instead 
of  running  them  with  gear-wheels,  and  that  they  run  much  lighter, 
stiller,  and  with  far  less  friction,  and  a  proportionately  less  motive 
power,  with  belts  than  with  gear-wheels." 

"  A  cotton-mill  of  dimensions  adapted  to  the  convenient  operation 
of  4000  spindles  of  cotton  machinery,  including  all  the  preparation 
for  making  yarn  and  weaving  cloth,  ordinarily  required  four  trains 
of  upright  shafts,  extending  through  the  height  of  four  stories,  the 
trains  usually  commencing  in  the  basement  story." 

"  To  each  train  of  uprights  were  attached  from  two  to  four  pairs 
of  heavy  gear-wheels,  and,  in  addition  to  these,  in  many  mills  all  the 
counter  lines  of  shafts  were  geared  off  at  right  angles  with  the  hori- 
zontal main  shaft,  which  required  a  very  large  number  of  gears  and 
shafts.  A  mill  thus  geared  is  a  full  load  for  the  power  of  a  moderate 
sized  water-wheel  without  any  machinery,  and  a  great  proportion  of 
this  unnecessary  weight  and  friction  may  be  saved  by  the  judicious 
use  of  belts  instead  of  gears.  And  besides  the  disadvantages  before 
named,  the  trains  of  gear-wheels  require  the  constant  extra  expense 
of  careful  attendance  and  of  oil  or  some  unctuous  matter  to  lubricate 
and  keep  them  from  heating,  friction,  and  abrasion.  And  again,  all 
the  gears  must  be  closely  boxed  in,  and  supplied  with  tight  dripping- 
pans,  or  the  mill-grease  will  be  liable  to  drop  into  the  work,  and 
greatly  damage  if  not  entirely  ruin  it. 


62  RULES    FOR    BELTINQ. 

tity  more  than  the  loaded  pulley,  to  put  the  greater  strain  upon  the 
belt,  and  the  amount  of  slack  is  increased  correspondingly. 

"  Hence,  in  a  narrow  belt  the  returning  part  will  be  slacker  than 
when  a  broader  belt  is  employed,  because  it  will  stretch  more  with  a 
given  tension. 

"  Short  belts  require  to  be  tighter  than  long  ones.  A  long  belt, 
working  horizontally,  increases  the  tension  by  its  own  weight,  acting 
in  the  curve  formed  between  the  pulleys. 

"  One  of  the  properties  of  this  curve  is  to  make  the  tension  greater 
than  is  due  to  the  simple  weight  of  the  belt ;  that  is  greater  than  when 
the  belt  is  hanging  vertically  ;  besides,  it  never  loses  contact. 

"  In  vertical  belts  so  little  stretch  is  needed  to  make  them  lose 
contact  with  the  lower  pulley,  that  the  tension  for  the  state  of  rest 
requires  to  be  greater  than  is  found  necessary  for  a  horizontal  belt, 
if  the  breadth  be  not  increased  to  reduce  the  stretching  stress  per  sec- 
tional square  inch. 

"  In  ordinary  leather  belts,  on  large  pulleys,  the  bending  resistance 
is  so  small  that  it  may  be  disregarded. 

"  Ropes  of  hemp  or  wire  are  often  employed  for  driving  bands. 
Their  resistance  to  bending  is  greater  than  that  of  flat  leather  belts, 
and  as  the  surface  in  contact  with  the  pulling  is  less,  the  pressure  per 
square  inch  of  actual  contact  must  be  greater,  and  therefore  more 
severe  upon  the  material. 

"  This,  however,  does  not  affect  the  amount  of  tension  required  for 
work,  because,  as  friction  is  independent  of  the  extent  of  surface,  we 
get  the  same  driving  power  from  10  Ibs.  pressure  or  tension  on  the 
narrow  line  of  contact  with  the  pulley,  in  the  case  of  a  circular  rope, 
that  we  would  get  from  the  same  pressure  supposing  the  rope  flat- 
tened out  so  as  to  have  a  surface  of  contact  many  times  greater. 

"  When  we  know  the  weight  per  foot  of  a  long  belt  or  rope  work- 
ing horizontally,  we  find  the  tension  in  the  curve  of  the  belt  between 
the  pulleys  by  multiplying  the  whole  weight  of  the  part  between  the 
pulleys  by  the  distance  between  the  same,  and  dividing  by  eight  times 
the  deflection.  This  rule,  however,  applies  only  to  curves  in  which 
the  deflection  is  small  compared  with  the  span  ;  so  that  the  flatter  the 
angle  of  suspension  the  closer  the  approximation." 

I.  H.  Beard  on  Belts. 

55.  u  Throughout  New  England,  until  within  a  few  years,  it  was 
generally  thought,  by  engineers  and  millwrights,  that  cotton-mills  and 
woollen-mills,  and  all  others  requiring  a  very  considerable  power, 


RULES    FOB    BELTING.  63 

could  not  be  run  effectively  without  large  and  ponderous  lines  of 
upright  and  horizontal  shafts  of  either  cast  or  wrought  iron,  and 
heavy  trains  of  cog-wheels  of  cast  iron,  or  partly  of  iron  and  partly 
of  wood. 

"And  when  large  leather  belts  began  to  be  introduced  for  the  main 
gear  of  mills,  as  a  substitute  for  gear-wheels,  it  was  thought  by  some 
of  our  best  engineers  to  be  an  experiment,  at  the  least,  of  very  doubt- 
ful result,  if  not  altogether  impracticable ;  and,  indeed,  at  the  present 
time  (1837),  notwithstanding  all  the  evident  advantages  of  belts  over 
gear-wheels,  many  still  adhere  to  the  old  mode  of  gearing ;  and  this, 
doubtless,  not  so  much  from  a  want  of  discernment  and  sound  judg- 
ment, as  from  a  lack  of  opportunity  of  comparing  and  testing  the 
advantages  of  belts  and  the  disadvantages  of  gear-wheels ;  or,  per- 
haps, they  may  have  formed  an  erroneous  opinion  of  the  utility  of 
using  belts  from  the  inspection  of  some  mills  that  have  been  belted 
on  a  bad  principle,  or  from  belts  injudiciously  managed." 

"  Having,  from  a  constant  practical  experience  of  both  modes  of 
gearing  mills,  for  more  than  ten  years,  at  Lowell,  Saco,  and  other 
places,  become  fully  satisfied  of  the  utility  of  belting  mills,  instead 
of  running  them  with  gear-wheels,  and  that  they  run  much  lighter, 
stiller,  and  with  far  less  friction,  and  a  proportionately  less  motive 
power,  with  belts  than  with  gear-wheels." 

"  A  cotton-mill  of  dimensions  adapted  to  the  convenient  operation 
of  4000  spindles  of  cotton  machinery,  including  all  the  preparation 
for  making  yarn  and  weaving  cloth,  ordinarily  required  four  trains 
of  upright  shafts,  extending  through  the  height  of  four  stories,  the 
trains  usually  commencing  in  the  basement  story." 

"  To  each  train  of  uprights  were  attached  from  two  to  four  pairs 
of  heavy  gear-wheels,  and,  in  addition  to  these,  in  many  mills  all  the 
counter  lines  of  shafts  were  geared  off  at  right  angles  with  the  hori- 
zontal main  shaft,  which  required  a  very  large  number  of  gears  and 
shafts.  A  mill  thus  geared  is  a  full  load  for  the  power  of  a  moderate 
sized  water-wheel  without  any  machinery,  and  a  great  proportion  of 
this  unnecessary  weight  and  friction  may  be  saved  by  the  judicious 
use  of  belts  instead  of  gears.  And  besides  the  disadvantages  before 
named,  the  trains  of  gear-wheels  require  the  constant  extra  expense 
of  careful  attendance  and  of  oil  or  some  unctuous  matter  to  lubricate 
and  keep  them  from  heating,  friction,  and  abrasion.  And  again,  all 
the  gears  must  be  closely  boxed  in,  and  supplied  with  tight  dripping- 
pans,  or  the  mill-grease  will  be  liable  to  drop  into  the  work,  and 
greatly  damage  if  not  entirely  ruin  it. 


64  KULES    FOR    BELTING. 

"  These  are  serious  inconveniences  and  evils  that  may  be  avoided 
by  substituting  belts  in  place  of  gear-wheels.  The  first  expense  and 
the  constant  repairs  will  be  as  little  with  belts  as  with  gear-wheels, 
and  the  risk  and  hindrance  that  may  be  caused  by  belts  are  far  less ; 
for  if  a  main  belt  breaks,  it  is  the  work  of  a  few  minutes  only  to 
repair  it  or  replace  it  with  a  new  one,  whereas  the  breakage  of  a 
single  gear-wheel  may  cause  the  hindrance  of  a  week,  and  the  almost 
entire  loss  of  the  wheel  broken,  together  with  a  hundred  times  the 
labor  and  expense  in  exchanging  the  broken  wheel  for  the  new  one 
that  would  be  caused  in  repairing  or  exchanging  the  belts.  And, 
again,  if  it  should  be  found  desirable  at  any  time  to  change  the 
velocity  of  any  part  of  the  mill  gear,  it  is  much  more  easily  done, 
and  with  far  less  expense,  by  varying  the  size  of  the  pulleys  and 
drums  than  by  changing  gear-wheels." 

"  But  to  gear  a  mill  wholly  with  belts,  and  to  do  it  judiciously  and 
to  the  best  advantage,  doubtless  requires  more  nice  calculation,  care- 
ful judgment,  and  practical  experience  than  to  do  it  with  gear-wheels; 
for  many  mills  have  been  so  belted  as  to  cause  more  friction,  trouble, 
and  expense  than  would  be  caused  or  required  in  the  use  of  gear- 
wheels." 

Therefore,  to  enable  those  who  may  wish  to  calculate  mill-gear, 
and  who  may  not  have  had  the  means  in  forming  a  correct  judgment 
by  practical  experience,  to  judge  correctly  of  the  advantages,  as  well  as 
of  the  disadvantages,  of  several  modes  of  gearing,  I  shall  first  introduce 
such  modes  as  I  consider  objectionable,  and  then  bring  forward  a 
mode  that  I  consider  the  least  objectionable  and  the  best  now  in  use. 
To  know  how  to  avoid  an  evil  is  frequently  as  beneficial  as  to  know 
how  to  remedy  it. 

"  In  Fig.  9  A  represents  the  main  driving-pulley,  geared  from  and 
driven  by  the  water-wheel,  and  is  made  from  8  to  12  feet  in  diameter ; 
B  the  water-wheel ;  C  the  basement ;  D  the  carding-room ;  E  the 
spinning-room  ;  F  the  weaving-room ;  G  the  dressing-room. 

"a,  b,  c,  d,  e,f,  g,  h,  i,  andj,  represent  the  lines  of  drums  in  the 
carding  and  weaving  rooms.  These  lines  of  drums  extend  very 
nearly  the  whole  length  of  the  mill  inside,  and  for  a  mill  of  4000 
spindles  are  driven  by  two  belts  operating  in  the  same  manner.  1, 
2,  3,  and  4,  represent  the  belt-binders  to  lead,  or  bind,  the  belt  in  the 
required  directions. 

"  The  belt  here  represented  must  be  about  320  feet  long,  and  from 
12  to  15  inches  wide,  and  will  require  from  600  to  700  Ibs.  of  stout 
belt  leather  to  make  it.  These  belts  are  bulky,  ponderous,  and  un- 


RULES    FOR    BELTING 


65 


manageable ;  and  whenever  a  lacing  breaks,  to  which  accident  they 
are  frequently  liable,  they  are  likely  to  run  nearly,  or  quite  off,  of 
the  drums,  and  it  would  cause  the  hindrance  of  the  whole  work  of 
the  machinery,  and  the  work  of  some  half  a  dozen  men  half  a  day 
to  put  one  of  them  on  again." 


Fig.  9. 

"  In  laying  out  the  gear  of  a  mill,  it  is  worth  much  time  and  pains 
to  arrange  the  drums  and  belts  in  such  a  manner  that,  so  far  as  may 
be  practicable,  the  stress  of  one  belt  upon  the  journals  shall  be 
counteracted  by  that  of  another  belt  in  an  opposite  direction,  refer* 
ring  to  the  stress  upon  the  line  of  main  drums,  the  counter  drums 
5 


66  RULES    FOR    BELTING. 

being  of  minor  consequence ;  but  where  the  main  power  is  to  be  ex- 
erted to  throw  the  stress  upon  one  belt  into  that  of  another,  is  economy 
in  the  wear  of  the  whole  mill  gear,  as  well  as  in  power,  both  of  which 
are  points  of  great  importance  to  the  manufacturer.  This  point  has 
not  always  been  observed;  for  it  is  sometimes  more  convenient  in 
arranging  the  gear  and  machinery  of  a  mill  to  place  the  line  of  main 
drums  upon  one  side  of  the  mill  instead  of  in  the  centre.  And  the 
effect  of  this  arrangement  is  to  throw  the  whole  stress  of  the  belts 
upon  one  side  of  the  journals  of  the  main  drum  shafts,  which  ought 
ever  to  be  avoided." 

.  .  .  "  It  is  further  of  great  importance  that  each  belt  should 
be  of  such  a  length  that  it  will  adhere  to  the  drum  so  much  as  to 
prevent  it  from  slipping,  and  that  without  the  necessity  of  pulling 
on  the  belt  so  tight  as  to  cramp  the  drums  and  wear  the  bearings. 
Every  belt,  to  run  easy  and  well,  should  be  so  slack,  when  running, 
that  the  slack  side  should  run  with  a  waving,  undulating  motion, 
without  any  tension  except  on  the  leading  side,  and  when  belts  will 
so  run  without  slipping  upon  the  drums  or  pulleys,  they  will  wear 
for  a  great  length  of  time ;  for  although  a  belt  may  be  heavily  loaded, 
yet,  if,  at  every  revolution,  it  can  have  an  opportunity  for  relief  from 
its  tension  so  as  to  contract  to  its  natural  texture,  it  will  prevent  it 
from  breaking  by  the  stress  upon  it.  But  if,  otherwise,  it  be  kept 
strained  so  tensely  as  to  be  constantly  strained  to  its  greatest  extent 
on  both  sides  of  the  drums,  it  will  wear  but  a  short  time  without 
cracking  at  the  edges,  and  will  shortly  be  destroyed." 

"  Sufficient  care  is  seldom  taken  to  have  belts  to  run  free  and  easy, 
and  it  has  been  one  of  the  greatest  errors,  more  or  less  prevalent  in 
all  cotton  or  woollen  mills,  to  run  the  belts  so  tense  as  greatly  to  in- 
jure the  belts  and  rapidly  increase  the  wear  of  the  bearings." 

"  It  has  been  customary  in  almost  all  belted  mills  to  affix  heavy 
cast-iron  or  wooden  binders  (tighteners)  weighted,  to  the  belts  which 
drive  the  main  mill  gear,  to  prevent  them  from  slipping,  and  it  has 
been  generally  thought  impracticable  to  keep  them  from  slipping  on 
the  pulleys  and  drums  without  binders ;  but  this  opinion  is  wholly 
erroneous,  and  without  any  true  foundation,  if  the  belts  are  properly 
prepared  and  pulleys  and  shafts  arranged  so  that  the  belts  pull  against 
one  another,  and  thus  relieve  the  shaft  bearings  of  much  of  the  strain 
as  when  they  pull  the  same  way." —  Journal  Franklin  Inst.,  1837. 


RULES    FOR    BELTING.  67 

Wrapping  Connectors.— From  "  Fairbairn's  Mills  and  Mill  Work/1 
London,  1865,  p.  I,  Part  II. 

56*  "Considerable  difference  of  opinion  exists  as  to  the  best 
and  most  effective  principle  of  conveying  motion  from  the  source  of 
power  to  the  machinery  of  a  mill.  The  Americans  prefer  leather 
straps,  and  large  pulleys  or  riggers. 

"  In  this  country,  and  especially  in  the  manufacturing  districts, 
toothed  wheels  are  almost  universally  employed. 

"In  some  parts  of  the  South,  and  in  London,  straps  are  extensively 
used  ;  but  in  Lancashire  and  in  Yorkshire,  where  mill  work  is  carried 
out  on  a  far  larger  scale,  gearing  and  light  shafts  at  high  velocities 
have  the  preference. 

"  Naturally,  I  am  of  the  opinion  that  the  North  is  right  in  this 
matter,  and  that  consistently,  as  I  was  to  a  great  extent  the  first  to 
introduce  that  new  system  of  gearing  which  is  now  general  through- 
out the  country,  and  to  which  I  have  never  heard  any  serious  objec- 
tion, I  have  been  convinced  by  a  long  experience  that  there  is  less 
loss  of  power  through  the  friction  of  the  journals,  in  the  case  of 
geared  wheel  work,  than  when  straps  are  employed  for  the  trans- 
mission of  motive  power.  Carefully  conducted  experiments  confirm 
this  view,  and  it  is  therefore  evident  which  mode  of  transmission  is, 
as  a  general  rule,  to  be  preferred." 

"There  are  certain  cases  in  which  it  is  more  convenient  to  use 
straps  instead  of  gearing.  With  small  engines  driving  saw-mills, 
and  some  other  machinery  where  the  action  is  irregular,  the  strap  is 
superior  to  wheel  work,  because  it  lessens  the  shocks  incidental  to 
these  descriptions  of  work.  So,  also,  when  the  motive  power  has 
been  conveyed  by  wheel  work  and  shafting  to  the  various  floors  of  a 
mill,  it  is  best  distributed  to  the  machines  by  means  of  straps." 

"  In  some  of  the  American  cotton  factories,  however,  there  is  an 
immense  drum  on  the  first  motion,  with  belts  or  straps  from  2  to  3 
feet  wide,  transmitting  the  power  to  various  lines  of  shafting,  and 
these  in  turn,  through  other  pulleys  and  straps,  giving  motion  to  the 
machinery. 

"  From  this  description  it  will  be  seen  that  the  whole  of  the  mill 
is  driven  by  straps  alone,  without  the  intervention  of  gearing. 

"  The  advantages  of  straps  are  the  smoothness  and  noiselessness 
of  the  motion.  Their  disadvantages  are  cumbrousness,  the  expense 
of  their  renewal,  and  the  necessity  for  frequent  repairs.  They  are 
inapplicable  in  cases  where  the  motion  must  be  transmitted  in  a  con- 


68  RULES    FOK    BELTING. 

stant  ratio,  because,  as  the  straps  wear  slack,  they  tend  to  slip  over 
the  pulleys,  and  thus  lose  time.  In  other  cases,  as  has  been  observed, 
this  slipping  becomes  an  advantage,  as  it  reduces  the  shock  of  sudden 
strains,  and  lessens  the  danger  of  breaking  the  machinery. 

"Very  various  materials  are  employed  for  straps,  the  most  ser- 
viceable of  all  being  leather  spliced  with  thongs  of  hide  or  by 
cement.  Gutta-percha  has  been  employed  with  the  advantage  of  dis- 
pensing with  joints,  but  it  is  affected  by  changes  of  temperature,  and 
it  stretches  under  great  strains.  Flat  straps  are  almost  universally 
employed,  in  consequence  of  the  property  they  possess  of  maintaining 
their  position  on  pulleys,  the  faces  of  which  are  slightly  convex. 

"  Round  belts  of  cat-gut  or  hemp  are  sometimes  used,  running  in 
grooves,  which  are  better  made  of  a  triangular  than  a  circular  sec- 
tion —  so  that  the  belt  touches  the  pulley  in  two  lines  only,  tangen- 
tial to  the  sides  of  the  groove  ;  in  this  case  the  friction  of  the  belt  is 
increased  in  proportion  to  the  decrease  of  the  angle  of  the  groove." 

"The  strength  of  straps  must  be  determined  by  the  work  they 
have  to  perform.  Let  a  strap  transmit  a  force  of  n  horse-power  at 
a  velocity  of  v  feet  per  minute,  then  the  tension  on  the  driving  side 

0<3  f)f)f)  ,vj 

of  the  belt  is  —  '  —     —  Ibs.,  independent  of  the  initial  tension  pro- 

ducing adhesion  between  the  belt  and  pulley.  For  example,  let  v  be 
314.16  Fpm,  or  the  velocity  of  a  24-inch  pulley  at  50  Rpm,  and  let 


\y     Q 

3  horse-power  be  transmitted,  then   -  -  —  312  Ibs.,  the  strain 


on  the  pulley  due  to  the  force  transmitted." 

"The  following  table  has  been  given  for  determining  the  least 
width  of  straps  for  transmitting  various  amounts  of  work  over  differ- 
ent pulleys.  The  velocity  of  the  belt  is  assumed  to  be  between  25 
and  30  feet  per  second,  and  the  widths  of  the  belts  are  given  in 
inches.  With  greater  velocities  the  breadth  may  be  proportionably 
decreased." 

The  following  formula  will  meet  every  requirement  of  the  table  : 

w==  5940  HP 
1650  d 

In  which  W=  width  of  belt  in  inches. 
"       HP  =  horse-power. 

d  =  diameter  of  smaller  pulley  in  feet. 
"     1650  =  average  speed  in  feet  per  minute, 


RULES    FOR    BELTING.  69 

from  statement  above,  and  which  might  be  changed  for  v  =  velocity 
of  belt  in  Fpm  to  make  the  rule  more  general,  which  would  seem  to  be 
allowed  by  the  closing  paragraph  of  the  quotation. 

The  use  of  d  in  this  formula  forbids  the  naming  of  any  definite 
area  of  belt  running  per  horse-power  per  minute.  If  we  take,  how- 
ever, the  cases  of  belts  from  12  inches  to  24  inches  wide  on  a  6-feet 
pulley,  transmitting  from  20  to  40  horse-power,  and  giving  82^  square 
feet  of  belt  per  minute  per  horse-power,  we  would  not  be  stepping 
outside  the  line  of  usual  good  practice  in  selecting  average  examples 
from  the  table.  But  if  we  select  from  one  extreme  of  the  table  a  1.4 
inch  belt  running  on  a  10-feet  pulley,  transmitting  4  horse-power,  or 
48.125  square  feet  of  belt  per  minute  per  horse-power,  we  will  find 
it,  if  not  out  of  the  limits  of  possibility,  certainly  not  within  the  ordi- 
nary economy  of  practice  as  to  width  of  belt  and  diameter  of  the 
pulley.  On  the  other  extreme,  the  proportion  of  a  43.2  inch  belt, 
running  on  a  12-inch  pulley,  and  transmitting  12  horse-power,  or, 
measuring  off  495  square  feet  of  belt  per  minute  per  horse-power,  is 
such  an  excessive  one  that  perhaps  it  never  has,  and  certainly  never 
should  be  used  in  practice. 

From  J.  Richard's  "  Treatise  on  Wood  Machinery." 
E.  &.  F.  N.  Spon,  London,  1872. 

87 •  "  Belting,  gearing,  and  unbalanced  pulleys  or  wheels  repre- 
sent transverse  strain,  which  must  be  a  matter  of  judgment  rather 
than  estimates.  It  would  be  folly  to  predicate  the  transverse  strain 
upon  a  shaft  as  being  simply  the  tension  of  belts,  or  the  strain  of  gear- 
wheels working  under  ordinary  conditions.  A  rule  in  the  author's 
practice  has  been  in  the  case  of  belts  to  provide  sufficient  strength 
in  shafts  and  supports  to  tear  them  asunder,  without  damage  to  the 
machinery.  This  is  the  only  safe  rule,  for  there  is  no  means  of  always; 
guarding  against  winding  belts. 

"  Calling  the  distance  between  the  hangers  or  bearings  b,  the  diam- 
eter of  the  shaft  d,  and  width  of  belt  w,  a  rule  for  ordinary  cases 
would  be  w  =  d2  and  d  X  25  =  b.  This  is,  of  course,  arbitrary; 
and  presuming  the  pulleys  to  be  in  the  centre  between  the  bearings, 
and  not  more  than  five  faces  in  diameter.  In  proportioning  shafts 
for  belting,  much  must  be  left  to  judgment,  and  be  dictated  by  that 
peculiar  sense  of  realizing  what  is  wanted  from  previous  experience. 

"  There  are,  in  fact,  so  many  obscure  conditions  that  have  to  do 
with  the  matter,  that  any  rule  must  be  an  arbitrary  one,  if  given  for 
general  application.  The  above  is,  however,  safe,  so  far  as  strength 


70  RULES    FOB    BELTING. 

is  concerned,  for  gearing,  shafts  must,  as  a  rule,  be  stronger  than  for 
belts.  The  motion  is  positive,  and  lacks  the  elasticity  that  exists  in 
belt  connections.  Shafts  are  in  general  made  strong  enough  to  crush 
cast-iron  gearing ;  practice  has  given  larger  proportions  to  shafts  that 
receive  gearing,  no  doubt  for  the  reasons  stated,  that  of  positive  mo- 
tion ;  yet  the  proper  plan  in  the  construction  of  wood  machines  would 
in  all  cases  be  to  drive  the  first  movers  with  belting  so  proportioned 
and  arranged  that  it  would  be  sure  to  yield  before  breaking  the  gear- 
ing. Ordinary  belting,  with  its  surfaces  dry,  as  they  must  be  when 
operated  on  wood-working  machines,  has  much  less  driving  power 
than  the  belting  on  metal-working  machines,  when  the  surfaces  be- 
come covered  with  oil  or  gum,  and  the  leather  soft  and  pliable.  As- 
suming the  belts  to  be  dry,  a  good  rule  for  belting  and  gearing  for 
feeding  wood  machines  would  be  as  follows :  Let  V  be  the  velocity 
of  the  belt,  and  v  that  of  the  pinion  or  first  mover,  the  width  of  the 

belt  to  be  the  same  as  that  of  the  gearing  —  =  v;  or,  in  other  words, 

the  diameters  of  the  pulleys  to  be  to  the  pinion  as  6  to  1,  with  equal 
faces :  variations  as  to  relative  width  should  be  directly  as  the  pro- 
portion between  pinion  and  pulley ;  if,  for  instance,  the  face  of  the 
pinion  was  reduced  to  2  inches,  and  the  belt  remain  3  inches  wide, 
their  velocities  would  require  to  be  v  x  4  =  V,  or  diameter  as  1  to 
4,  the  diameter  of  the  shaft  being  equal  to  the  square  root  of  the  face 
of  the  pulley.  There  would  with  these  proportions  be  no  danger  of 
breaking  either  shafts  or  gearing,  it  being  understood,  of  course,  that 
in  a  train  of  gearing  such  as  is  used  in  planing-machines,  the  force 
and  pitch  of  each  wheel  and  shaft  should  be  inversely  as  their 
velocity. 

"  The  belting  for  circular  saws  is,  as  a  rule,  too  narrow,  or  upon 
pulleys  of  too  small  diameter.  To  drive  a  saw  well  and  without  in- 
jurious strain  upon  the  bearings,  belts  should  be  one-third  the  diam- 
eter of  the  saw  in  width,  and  the  pulley  equal  in  diameter  to  the 
width  of  the  belt,  which  is  a  very  simple  rule,  and  does  not  give  any 
more  than  the  needed  driving  force,  under  fair  conditions. 

"  One-fourth  the  diameter  of  the  saw  for  the  diameter  of  pulleys 
on  cross-cutting  spindles.  Their  faces  can  be  one  and  a  half  diam- 
eter in  length. 

"  That  speed  should  be  an  element  in  estimating  belt  contact  is 
apparent  in  looking  at  the  spindle  pulleys  in  wood-cutting  machines. 
The  degree  in  which  belts  are  affected  by  centrifugal  force  in  running 
at  high  speed  is  dependent  upon  the  tension,  weight,  and  flexibility 


RULES    FOR    BELTING.  71 

of  the  belt  and  the  diameter  of  the  pulley.  At  5000  feet  a  minute, 
with  belts  of  ordinary  harness  leather,  running  on  pulleys  six  inches 
or  less  diameter,  the  amount  of  contact  is  not  more  than  three-fifths 
of  what  would  be  shown  in  a  diagram,  and  is  often  much  less.  Cou- 
pled with  this,  however,  is  the  strange  fact  that  the  tractive  force 
does  not  seem  to  be  as  constant  as  the  amount  of  contact.  That  the 
pressure  on  so  much  of  the  surface  as  has  contact  is  increased  by  the 
belt  lifting,  is  unquestionably  the  case,  but  it  hardly  accounts  for 
the  want  of  proportion  between  the  power  transmitted  and  the  amount 
of  contact.  This  matter  is  mentioned  as  an  experimental  fact,  and 
merely  to  stand  as  a  reason  for  saying  that  the  width  of  the  belts 
need  not  be  predicated  directly  upon  the  pulley  contact  for  high 
speed  spindles. 

"  For  spindles  having  unusually  high  speeds,  the  writer  has  found 
belts  of  cotton  webbing  to  be  preferable.  Such  belts,  if  closely  woven 
and  of  the  best  material,  will,  when  waxed,  be  found  to  have  a  high 
tractile  power  and  wear  well,  while  their  comparatively  light  weight 
avoids  their  lifting  from  centrifugal  force. 

"  The  convexity  of  pulleys  to  keep  belts  central  should  be  suffi- 
cient for  the  purpose,  and  no  more.  It  is  difficult  to  account  for  the 
practice  of  many  builders  of  wood  machines,  especially  in  England, 
who  give  a  degree  of  convexity  to  pulleys  that  interferes  with  the 
contact  and  tends  to  the  destruction  of  the  belt,  unless  both  pulleys 
have  their  faces  the  same,  a  thing  impossible  in  the  case  of  shifting 
belts.  Without  entering  into  an  examination  of  the  laws  and  condi- 
tions that  govern  the  matter,  the  following  rule  is  given : 

"  For  pulleys  from  2  to  24  inches  face,  the  convexity  should  be 
from  |  to  yg-th  of  an  inch  to  a  foot,  graduated  inversely  as  the  width 
of  the  faces ;  for  pulleys  of  narrower  face,  the  convexity  can  be 
slightly  increased. 

"This  is  quite  sufficient  to  govern  the  running  of  belts,  and  a 
necessity  for  more  can  safely  be  construed  as  a  fault  in  the  position 
of  the  shafting. 

Mr.  James  Christie,  of  Pittsburgh,  gives  the  following : 

58*  "  I  can  give  an  example  of  engine  and  connected  belting, 
during  the  performance  of  which  I  had  frequent  opportunities  of 
observation. 

"  The  engine  has  a  cylinder,  8-inch  diameter  by  12-inch  stroke, 
and  made  150  Rpm  under  a  boiler  pressure  of  75  Ibs.  to  the  square 
inch,  and  piston  pressure  of  40  Ibs.,  doing  an  effective  service  of  18 


72  RULES    FOR    BELTING. 

horse-power.  It  drove  a  brick  machine  by  a  first-class  double  leather 
belt,  6-inch  wide  and  nearly  f-inch  thick,  laced  in  the  usual  way. 
The  smooth  turned  iron  driving  pulley  Or  engine  shaft  is  22-inch 
diameter ;  the  driven  pulley,  of  like  material  and  finish,  on  brick 
machine,  48-inch  diameter ;  distance,  horizontally,  between  shafts,  12 
feet ;  top  fold  of  the  belt  slack,  no  tightener  applied,  belt  was  well 
stretched,  no  resin  or  unguent  used. 

"  Both  engine  and  belt  were  insufficient  for  the  purpose,  but  I  con- 
sidered each  about  the  equal  of  the  other.  When  first  used  the  en- 
gine would  drive  ahead  and  slip  the  belt ;  as  belt  and  pulley  became 
more  attached,  and  belt  was  tightly  laced,  the  belt  would  '  stall '  the 
engine." 

The  above  gives  24.27  square  feet  of  belt  per  horse-power  per  min- 
ute, and  114.8  pounds  strain  to  one  inch  width  of  belt,  and  may  be 
considered  as  a  very  reliable  example  of  a  hard-worked  belt. 

"  In  driving  8-iuch  trains  of  rolls,  the  practice  here  is,  when  driv- 
ing direct,  to  use  engines  of  from  12  to  16-inch  diameter  of  cylinder, 
similar  in  construction  to  the  usual  slide-valve  engines  the  country 
over,  and  working  under  a  boiler  pressure  of  say  90  Ibs.  to  the  square 
inch,  and  average  piston  pressure  of  50  Ibs.  The  12-inch  cylinders 
have  proved  inadequate,  the  14-inch  have  ample  power,  and  the  16- 
inch  have  an  overplus. 

"  The  piston  speed  of  these  engines  is  invariably  high,  seldom  less 
than  400  Fpm,  frequently  600  and  700,  and  sometimes  as  high  as  800. 

"  14-inch  belts  have  proved  insufficient  in  driving  such  a  train, 
16-inch  do  very  well,  and  18-inch  are  wider  than  needed.  The  16 
and  18-inch  are,  however,  commonly  used,  and  are  always  double 
leather,  or  two  or  three-ply  gum  belts. 

"  When  driven  from  line  shaft,  which  is  the  usual  plan,  6-feet  pul- 
leys are  used,  both  on  line  and  on  rolls,  say  25  feet  between  centres, 
and  the  angle  of  belts  with  a  vertical  line  about  20°.  Sometimes  the 
pulley  on  rolls  is  made  heavy,  but  commonly  separate  fly-wheels,  of 
about  8  feet  diameter  and  4  tons  weight,  are  used.  Tighteners  are 
seldom  employed,  speed  of  rolls  from  150  to  250  Rpm. 

"  In  a  steel  mill  here,  a  20-feet  fly-wheel  pulley  on  engine  shaft, 
running  at  60  Rpm,  drives  a  6-feet  pulley,  4  tons  weight,  on  the  train 
at  20  feet  distant,  between  shafts,  horizontally.  The  train  is  a  9-inch 
one,  belt  17  inches  wide,  of  three-ply  gum,  and  no  tightener  used. 

"  The  belt  slips  while  rolling  long  lengths,  which  would  indicate 
insufficient  momentum  in  and  lack  of  belt  contact  on  the  fly-wheel 
pulley  on  the  train. 


RULES    FOB    BEL  TING.  73 

"  Greater  distance  apart  of  shafts  and  less  difference  of  diameters 
of  pulleys  would  give,  therefore,  a  better  belt  result. 

"  I  have  never  heard  of  any  objection  to  the  use  of  belts  in  rolling- 
mills  on  the  score  of  durability. 

"  In  order  to  obtain  the  full  value  of  a  belt,  it  is  first  necessary 
that  it  should  be  in  thorough  contact  with  the  pulleys.  A  new  belt 
will  be  found  touching  in  spots,  and  will  not  pull  well  for  want  of 
entire  contact  with  pulley.  Any  unguent  put  on  the  belt  will  be 
found  of  immediate  benefit,  as  it  softens  its  surface,  and  brings  it  in 
complete  contact  with  the  face  of  pulley.  The  hair  side  of  belt,  on 
account  of  its  smoothness  and  closeness  of  texture,  seems  to  conform 
to  this  necessary  condition  much  sooner  than  the  flesh  side,  which 
is  open  in  texture  and  rough  on  the  surface.  But  after  the  belt  is 
once  worn  to  the  proper  condition,  I  doubt  if  there  is  any  appreci- 
able difference  in  the  two  sides  in  value.  In  fact,  with  well-worn 
belts,  which  have  been  used  alternately  with  each  side  to  pulley,  it 
is  often  difficult  to  distinguish  the  hair  side  from  the  flesh  side.  By 
well  worn  I  do  not  mean  injured  by  use,  but  simply  that  condition  of 
belt  in  which  the  color  of  the  sides  is  rendered  uniform  by  absorption 
of  oil,  and  in  which  the  surface  gloss  and  texture  are  made  nearly  uni- 
form by  contact  with  pulleys.  Intimate  contact  between  belts  and 
pulleys  is  undoubtedly  necessary.  The  utility  of  smooth  faces  to 
pulleys  is  also  well  established." 

The  following  Notes  on  Belting  are  taken  from  Mr.  B.  F.  Sturte- 
vant's  Illustrated  Catalogue  of  Pressure- Blowers,  Boston,  Mass. 
SO.     "  Double  belts  are  calculated  to  be  |  of  an  inch  thick,  single 
belts  J  of  an  inch  thick.     The  holding  power  of  the  belt  is  governed 
wholly  by  its  tension  or  tightness  and  the  condition  of  its  surface,  the 
diameter  of  the  pulleys  having  nothing  to  do  with  it,  and  is  capable 
of  being  increased,  by  tightening,  to  350  Ibs.  to  one  square  inch  of 
cross  section. 

"  As  a  general  rule,  belts  running  from  a  large  to  a  small  pulley 
slip  on  the  large  and  not  on  the  small  one,  as  is  commonly  supposed. 
This  is  explained  as  follows :  The  pressure  per  square  inch  with  which 
the  belt  hugs  the  small  pulley  is  just  as  much  greater  as  the  small 
pulley  is  less  in  diameter  than  the  large  one,  and  the  friction  of  the 
belt  more  than  follows  the  increased  pressure.  For  example  :  If  you 
cover  the  small  pulley  on  the  counter  with  leather,  to  prevent  slipping, 
you  must  also  cover  the  driving  pulley  on  the  main  line,  or  you  get 
no  benefit  from  covering  the  small  pulley.  These  remarks  apply  to 
*  horizontal  belts. 


74 


RULES    FOR    BELTING. 


"  A  table  is  given  for  finding  the  width  in  inches  of  double  main 
belts  for  driving  his  patent  pressure-blowers,  which  is  based  on  the 
statement  that  a  belt  one  inch  wide,  having  a  velocity  of  1000  Fpm, 
will  give  one  horse-power.  This  is  also  equivalent  to  a  surface  velocity 
of  83^  square  feet  of  belt  per  minute  per  horse-power,  and  a  working 
strain  of  33  Ibs.  per  inch  width  of  double  belt,  or  99  Ibs.  per  square 
inch  of  cross  section  of  leather. 

"  New  belting,  such  as  is  generally  used  for  the  driving-belts  on 
polished  iron  pulleys,  will  only  transmit  from  one-third  to  one-fifth 
the  power,  without  slipping,  that  the  same  belt  will  after  it  has  been 
in  use  from  one  to  two  months. 

"  The  belts  for  driving  the  blowers  are  not  exposed  to  the  wear  and 
tear  of  shippers,  as  lathe  belts  are  ;  all  of  them  run  over  small  pulleys 
in  proportion  to  the  width  of  the  belts.  Hence  I  have  recommended 
a  scale  of  thicknesses  of  belts  in  proportion  to  the  widths..  The  lighter 
the  belt  the  tighter  it  hugs  the  pulley,  for  the  reason  that  all  unnec- 
essary weight  of  leather  tends  to  lift  itself  off  the  pulley  when  going 
around  it  at  a  greater  velocity,  and  some  of  these  belts  travel  at  a 
velocity  of  5000  Fpm. 

"  Belting,  as  it  is  generally  manufactured  as  an  article  of  merchan- 
dise, is  intended  for  all  purposes  for  which  belting  is  used ;  but  when 
parties  are  desirous  of  having  everything  about  the  blower  just  as  it 
should  be,  they  will  see  that  their  belts  are  made  exactly  to  suit 
their  work. 


No.  of 
Fan. 

Diam.  of 
Pulley. 

Face  of 
Pulley. 

Breadth 
of  Belt. 

Thickness 
of  Belt. 

Revs,  of  Fan 
per  min. 

Diam.  Driv- 
ing Pulley. 

HP  re- 
quired. 

00 

I7 

1J 

l\ 

-.08 

21 

0 

o  i 

if 

4 

.09 



21 

, 

1 

2-| 

2 

if 

.11 

4135 

21 

.5 

2 

3 

2| 

2 

.12 

3756            24 

1 

3 

3i 

2j 

2| 

.13 

3250            28 

1.8 

4 

4i 

Si 

2| 

.15 

3100 

32 

3 

5 

4| 

3f 

3i 

.16 

2900 

36 

5.5 

6 

5| 

4i 

3| 

.18 

2820 

42 

9.7 

7 

6| 

4 

44 

.20 

2600 

48 

16 

8 

7? 

6 

5| 

.22 

2270 

54 

22 

9 

91 

6J 

6 

.24 

2100 

48 

35 

10 

io| 

8 

7 

.25 

1815 

54 

48 

"  In  the  above  table  all  the  dimensions  are  in  inches.     To  give 
some  idea  of  the  proper  length  of  belt,  the  centre  of  the  driving 


RULES    FOR    BELTING.  75 

pulley  is  placed  3J  times  its  diameter  from  the  centre  of  the  fan  and 
2^  times  above  it.  The  driven  pulley  on  the  driving  pulley-shaft  is 
18  inches  diameter,  and  that,  in  turn,  is  driven  by  a  54-inch  diameter 
pulley  and  belt  of  double  thickness.  The  centres  of  the  54-inch  and 
18-inch  pulleys  are  placed  about  3  times  the  diameter  of  the  larger 
pulley  apart  and  nearly  at  same  height  from  floor." 

On  the  Creep  of  Belts. 

60.  "  It  is  generally  considered  by  those  who  have  had  experi- 
ence in  the  matter,  that  there  is  a  slight  slip  in  all  belts,  however 
large  they  may  be  in  proportion  to  the  power  transmitted,  and  however 
tightly  they  may  be  stretched.  Perhaps  in  the  case  in  which  a  belt 
is  much  larger  than  is  required,  it  would  be  better  to  say  that  there 
is  a  slight  creeping,  instead  of  a  slip,  this  creeping  being  caused  by 
the  change  in  tension  of  the  belt  as  it  moves  from  the  tight  to  the 
slack  side  in  passing  over  the  pulley. 

"  Where  belts  are  driven  at  a  high  velocity  it  is  found  that  the  cen- 
trifugal force  still  further  changes  the  ratio  of  speeds  of  the  driving 
and  driven  pulleys,  in  some  cases  decreasing  the  tension  of  the  belt, 
and  in  others  acting  in  the  contrary  way.  This  may  be  explained  in 
the  following  manner :  If  the  pulleys  over  which  the  belt  is  stretched 
are  quite  close  together,  the  two  parts  of  the  belt  will  be  nearly 
straight,  so  that  there  will  be  little  change  of  tension,  whether  the 
belt  is  at  rest  or  in  motion,  and  the  centrifugal  force  diminishes  the 
tension.  If  the  pulleys  are  a  considerable  distance  apart,  the  two 
portions  of  the  belt  will  be  curved,  and  part  of  the  centrifugal  force 
acts  in  increasing  the  length  of  the  belt,  and  thus  increases  the  ten- 
sion, instead  of  diminishing  it,  as  in  the  former  case.  In  ordinary 
cases,  where  the  velocity  of  a  belt  is  not  very  great,  it  is  probably 
not  necessary  to  consider  the  action  of  centrifugal  force. 

"  The  writer  is  frequently  engaged  in  making  tests  of  machinery, 
and  finds  it  convenient  to  obtain  a  record  of  the  speed  of  shafts  and 
engines.  At  a  recent  test  of  power  in  a  large  factory  some  inter- 
esting data  were  obtained  in  relation  to  the  creeping  of  belts,  and  it 
is  believed  that  these  results  may  be  of  interest  and  value  to  other 
engineers." 

The  case  was  one  in  which  the  size  of  the  belts  was  largely  in 
excess  of  that  actually  required  for  the  transmission  of  the  power,  and 
the  velocity  with  which  they  moved  was  quite  moderate.  Under 
these  circumstances  it  was  to  be  expected  that  the  difference  between 
the  actual  ratio  of  speeds,  and  that  which  should  have  been  obtained 


76 


RULES    FOR    BELTING. 


if  there  had  been  no  slip  or  creep,  would  be  less  at  an  increased  than 
at  a  diminished  rate  of  speed,  if  the  changes  in  speed  were  so  slight 
as  not  sensibly  to  vary  the  centrifugal  force.  For  the  purposes  of 
the  test,  counters  were  attached  to  the  driving  engine  and  to  the 
shaft  in  a  distant  part  of  the  building,  the  power  being  transmitted 
to  that  shaft  by  five  belts.  Simultaneous  readings  of  the  two  counters 
were  taken  every  minute  for  the  space  of  an  hour.  The  result  of  several 
of  these  observations  for  intervals  of  five  minutes  each  is  given  below : 


REVOLUTIONS 
OF  ENGINE. 

REVOLUTIONS 
OP  SHAFT. 

RATIO 
OF  SPEED. 

159 
153 
154 
148 

417 
397 
403 
383 

2.623 
2.595 
2.617 
2.588 

Total,  1848 

4816 

2.612 

"  It  will  be  observed  that,  as  the  speed  was  decreased,  there  was  a 
perceptibly  greater  creep  in  the  belts.  It  having  been  found  advis- 
able to  increase  the  speed  of  the  engine  and  shafting,  similar  tests 
were  made,  when  this  change  was  effected,  and  a  few  of  the  results 
are  given  below : 


REVOLUTIONS 
OF  ENGINE. 

REVOLUTIONS 
OF  SHAFT. 

RATIO 
OF  SPEED. 

205 

538 

2.624 

204 

535 

2.623 

203 

532 

2.621 

206 

541 

2.626 

208 

544 

2.615 

Total,  2457 

6432 

2.618 

"  It  is  generally  known  that  there  is  a  best  speed  for  a  belt  under 
given  conditions,  and  that,  if  this  speed  is  either  increased  or  dimin- 
ished, the  tension  of  the  belt  will  be  diminished.  It  appears,  from 
these  latter  results,  that  this  speed  was  about  reached  by  the  change, 
so  that  the  belts  were  transmitting  under  the  most  favorable  condi- 
tions as  regards  speed. 

"  A  careful  measurement  of  all  the  pulleys  transmitting  the  power 
from  the  engine  to  the  shaft  in  question,  increasing  their  diameters  by 
the  mean  thickness  of  the  belts  passing  over  them,  shows  that  the 


RULES    FOB    BELTING.  77 

actual  ratio  of  speeds  of  engine  and  shaft  should  have  been  as  1  to 
2.625,  so  that  there  was  an  average  slip  or  creep  in  the  first  case  of 
0.495  per  cent.,  and  in  the  second  0.267  per  cent. — R  H.  Buel,  M.  E., 
SO  Broadway,  N.  Y.,  The  Engineering  and  Mining  Journal,  February 
28,  1874. 

Leather  Pulley. 

61.  As  there  is  "  nothing  like  leather  "  for  many  purposes,  espe- 
cially in  places  where  there  is  much  rubbing  and  at  high  velocities, 
it  has  occurred  to  many,  perhaps,  and  the  transition  of  thought  seems 
natural  indeed,  that  if  leather  will  endure  so  much  wear  and  tear  at 
the  circumference  of  a  vheel,  it  must  resist  a  like  action  at  its  axle, 
and  therefore  it  would  make  a  good  bush  for  a  loose  pulley,  or,  where 
small,  the  whole  pulley  might  be  made  of  leather.     Accordingly,  this 
has  been  done  with  good  effect ;  leather  discs  were  bolted  together, 
bored  out,  turned  off,  soaked  in  oil,  and  put  in  place  as  if  made  of 
iron  in  the  usual  way. 

Driving  Power  of  Belts  Compared  with  that  of  Friction  Gear. 

62.  Newton's  Journal  for  1857,  Vol.  VI.,  New  Series,  p.  163, 
presents  Mr.  James  Robertson's  paper  on  grooved  surface  frictional 
gearing,  from  which  we  take  the  following : 

"  The  object  of  this  paper  is  to  describe  a  system  of  frictional  gearing 
recently  introduced  by  the  writer,  intended  chiefly  for  high  speeds, 
and  to  give  such  information  regarding  its  action  and  driving  capa- 
bilities as  the  several  applications  of  it  in  use  will  afford. 

"  The  grooved  surface  frictional  gearing  consists  of  wheels  or  pulleys 
geared  together  by  frictional  contact,  communicating  motion  indepen- 
dently of  teeth  or  cogs  ;  the  driving  surfaces  are  grooved  or  serrated 
annularly,  the  ridges  of  one  surface  entering  the  grooves  of  the  other. 
The  extent  of  contact  is  thus  increased  in  the  direction  of  the  breadth 
of  the  rim,  and  a  lateral  wedging  action  is  obtained,  which  augments 
the  effect  of  the  pressure  holding  the  wheels  in  gear,  the  necessary 
amount  of  which  is  felt  to  be  so  injurious  to  the  bearings  of  the  shafts 
when  the  power  is  communicated  by  plain  driving  surfaces. 

"  The  grooves  are  made  V-shaped,  and  are  found  to  suit  best  when 
formed  at  an  angle  of  about  50°.  The  pitch  of  the  grooves  is  varied 
to  the  velocities  of  the  wheels  and  the  power  to  be  transmitted ;  the 
smallest  pitch  employed  is  |-inch,  and  that  required  for  the  heaviest 
operations  about  f-inch.  The  ordinary  pitch  is  about  f-inch.  The 
wheels  are  turned  up  truly,  and  the  grooves  equally  pitched  and  made 
exactly  alike  on  each  face ;  so  that,  on  applying  the  surfaces  to  each 


78  RULES    FOE    BELTING. 

other,  a  well-fitted  contact  throughout  the  faces  is  obtained.  In  order 
to  increase  and  sustain  the  wedging  action,  the  points  of  the  ridges  are 
left  blunt,  to  prevent  them  from  reaching  the  bottom  of  the  grooves. 

"  Cast-iron  has  as  yet  been  the  only  material  used  in  the  construc- 
tion of  grooved  wheels,  and  its  action  has  been  found  so  satisfactory 
that  there  is  no  necessity  for  trying  any  other.  The  surfaces,  after 
working  a  short  time  together,  assume  a  smooth,  polished  appearance, 
taking  a  greater  hold  in  proportion  to  the  smoothness  they  acquire ; 
and  when  a  sufficient  breadth  for  the  speed  and  power  to  be  trans- 
mitted gets  into  contact,  there  is  afterwards  no  perceptible  tendency 
to  wear. 

.  .  .  "  The  points  that  have  to  be  attended  to,  so  far  as  the 
power  or  driving  contact  is  concerned,  are  the  angle  of  the  grooves 
and  the  pressure  holding  them  in  contact ;  the  extent  of  surface  in 
contact  being  determined  so  as  to  prevent  abrasion  and  withstand  the 
wearing  action.  .  .  .  Wheels  of  large  diameter  show  a  decided 
superiority  of  action. 

4<  In  order  to  obtain  a  high-speed  from  a  driving  belt,  without  the 
usual  arrangement  of  counter-shafts  and  belt-pulleys  between  the 
main  driving  shaft  and  the  machine  to  be  driven,  and  without  the 
disadvantage  of  passing  the  belt  over  a  small  pulley,  a  small  grooved 
pulley  is  keyed  on  the  shaft  to  which  the  high  velocity  is  to  be  com- 
municated, and  upon  it  is  placed  a  loose,  inflexible  ring,  of  two  or 
three  times  the  diameter  of  the  pulley,  grooved  internally  to  fit  it, 
and  turned  up  smoothly  on  the  outside  to  receive  the  driving  belt. 
The  belt  gives  motion  to  the  speed-ring,  the  inner  grooved  surface  of 
which  communicates  a  higher  speed  to  the  pulley.  The  speed-ring  is 
held  in  effective  driving  contact  simply  by  the  tension  of  the  belt. 
For  obtaining  increased  lateral  steadiness  at  high  speeds  a  double 
speed-ring  may  be  used  if  required.  By  these  arrangements  a  belt 
may  be  passed  over  a  speed-ring  of  16  inches  diameter,  and  yet  com- 
municate the  same  speed  to  the  shaft  as  if  it  were  passed  over  a  pul- 
ley of  only  4  inches  diameter. 

"  In  Fig.  10  the  driving  pulley,  D,  carries  a  belt,  B,  which  passes 
over  and  drives  the  speed-ring,  R,  of  large  diameter  as  compared 
with  the  small  grooved  wheel,  P,  increasing  circumferential  contact 
thereby. 

"  Enlarging  the  diameter  of  the  speed-ring  will  permit  the  driving 
pulley  to  be  placed  nearer  to,  without  altering  the  speed  of  the  driven 
wheel,  P,  and  will  also  increase  the  adhesion  and  driving  power  of 
the  belt. 


RULES    FOR    BELTING.  79 

"The  upper  'cut'  shows  an  enlarged  section  of  the  speed-ring 
exhibiting  its  grooves,  and  those  of  the  grooved  wheel,  P,  with  which 
it  is  engaged. 

"  Clutches  may  also  be  arranged  for  engaging  and  disengaging  by 
means  of  grooved  surfaces. 

"In  applying  this  system  of  driving,  where  a  reverse  motion  is 


Fig.  10. 

required,  a  disc,  having  an  outer  and  an  inner  rim,  is  keyed  to  the 
main  driving  shaft  —  the  outer  rim  grooved  on  the  inside,  and  the 
inner  rim  on  the  outside,  with  corresponding  grooves.  The  shaft  that 
is  to  be  driven  carries  a  small  grooved  pulley,  the  diameter  of  which 
is  slightly  less  than  the  distance  between  the  two  grooved  rims.  The 


80  RULES    FOR    BELTING. 

motion  of  this  pulley  will  be  reversed  by  moving  it  slightly  nearer 
to  or  farther  from  the  main  driving  shaft,  so  as  to  throw  it  into  gear 
with  the  inner  or  outer  rim  respectively.  ... 

"  For  comparing  the  pressure  required  to  hold  the  grooved  surfaces 
in  gear  and  the  power  transmitted,  various  opportunities  have  occurred 
in  the  actual  use  of  the  frictional  gearing,  and  arrangements  have 
been  made  for  purposes  of  experiment.  One  method  of  comparing 
its  driving  capabilities  with  those  of  belts  is  directly  obtained  by  the 
simple  speed-ring  movement  already  described  for  raising  high  speeds. 
One  of  these  speed-rings  has  been  working  satisfactorily  on  a  large 
foundry  fan  for  some  time ;  and,  from  the  circumstances  that  the  fan 
was  previously  driven  by  a  belt  of  the  same  size,  over  a  plain  pulley 
of  the  same  diameter  as  the  small  grooved  pulley  now  used,  this  case 
affords  a  certain  practical  means  of  comparing  the  efficiency  of  these 
two  methods  of  communicating  motion.  Before  the  application  of 
the  ring  the  belt  was  passed  over  a  pulley  6  feet  diameter,  keyed  on 
the  driving  shaft,  and  over  a  pulley  1\  inches  diameter  on  the  fan 
spindle;  but  the  continual  bending  of  a  large  heavy  belt  over  a 
pulley  of  so  small  diameter  made  it  difficult  to  keep  up  the  proper 
driving  tension,  and  the  belt  was  speedily  cut  up.  The  ring  now 
interposed  between  the  belt  and  pulley  is  13|  inches  diameter,  and 
saves  the  belt  from  injury  by  the  greater  diameter  over  which  it 
bends.  The  ring  works  steadily,  and  drives  the  fan  at  the  same  speed 
as  when  the  belt  was  passed  directly  over  the  small  pulley ;  thereby 
showing  that  the  grooved  metal  surface  does  not  strain  the  bearings 
more  than  the  ordinary  arrangement  of  driving  by  belts. 

"  Another  method  has  also  been  employed  for  comparing  the  driving 
capabilities  of  the  grooved-surface  gearing  with  those  of  belts,  by 
means  of  a  testing  apparatus,  having  the  same  pressure  on  the  bear- 
ings of  the  axis  as  is  produced  by  belts.  The  testing  apparatus  is 
made  by  gearing  together  two  spur  grooved  wheels,  each  21  inches 
diameter  and  3|  inches  face :  the  grooves  being  cut  |-inch  pitch,  and 
at  an  angle  of  50°.  Motion  was  communicated  to  the  driving  wheel 
by  a  7-inch  belt,  over  a  pulley  30  inches  diameter,  so  disposed  that 
there  was  no  pressure  to  hold  the  two  wheels  in  gear  but  the  pull  or 
strain  of  the  belt.  A  plain  friction  strap  wheel  was  keyed  on  the 
spindle  of  the  driven  wheel,  by  a  strap  and  break  handle  attached, 
so  that  it  could  be  either  retarded  or  stopped.  On  applying  the 
break,  it  either  caused  the  belt  to  slip  or  the  driving  engine  to  stop, 
without  the  grooved  wheels  showing  any  tendency  to  slip. 

"  There  is  a  slight  slip  in  the  rolling  action  of  the  grooved  wheels 


RULES    FOR    BELTING.  81 

which  does  not  occur  in  the  action  of  plain  surfaces,  which  arises 
from  the  difference  of  the  diameters  of  the  points  of  the  ridges  and 
bottoms  of  the  grooves ;  but  this  slipping  is  little  felt  in  practice, 
and,  when  measured,  is  inconsiderable  in  amount.  In  a  pair  of 
grooved  wheels,  8  feet  diameter  and  1  foot  broad,  with  24  grooves 
working  together,  there  is  a  slip  of  only  10  square  inches  in  an  entire 
revolution ;  whereas,  in  toothed  wheels  of  the  same  breadth  and 
diameter,  with  cogs  of  3-ineh  pitch,  of  the  ordinary  proportions, 
there  is  a  surface  to  slip  over  on  each  cog  of  about  24  square  inches, 
or  nearly  the  entire  area  of  one  side  of  the  cog ;  making  a  total  slip 
of  about  16  square  feet  in  every  revolution. 

"Lengthened  experience  is  necessary  to  ascertain  the  smallest 
breadth  of  face  that  will  be  sufficient  for  transmitting  a  given  amount 
of  power  without  abrasion  or  wearing  action  ;  and  it  is  therefore  pre- 
ferred at  present  to  make  the  grooved  wheels  broader  in  every  posi- 
tion than  seems  to  be  absolutely  necessary.  The  general  proportion 
of  toothed  wheels,  as  regards  both  breadth  of  face  and  other  dimen- 
sions, are  sufficiently  strong  for  transmitting  the  same  power  of 
grooved  surfaces ;  but  the  writer  is  of  opinion  that  less  breadth  of 
face  and  lighter  proportions  of  arms  and  rims  can  be  used  with  safety. 
If  the  grooved  wheels  are  employed  in  every  position  in  a  factory 
where  wheel  gearing  is  required,  no  shocks  or  jolting  action  can  take 
place ;  and  therefore  all  the  wheels  themselves,  and  also  the  shaftings 
and  supports,  may  be  made  much  lighter  than  can  be  used  with 
ordinary  gearing. 

"  One  of  the  principal  advantages  of  these  grooved  wheels  is  their 
smoothness  of  action,  in  positions  and  at  speeds  when  ordinary  toothed  * 
gearing  produces  a  disagreeable  jarring  noise,  their  action  is  scarcely 
audible." 

From  a  Circular  issued  by  P.  V.  H.  Van  Riper,  of  Paterson,  N.  J., 
we  select  the  following : 

63.  "Having  been  engaged  in  the  manufacture  of  oak  leather 
belting  for  the  past  fifteen  years,  I  would  respectfully  call  attention 
to  the  essential  points  necessary  to  the  manufacture  of  good  belting, 
the  first  of  which  is  the  selection  of  the  leather,  which  should  be  oak 
tanned,  it  being  more  pliable  than  any  other,  and  as  durability  is 
required,  it  should  be  thoroughly  tanned  and  made  from  young  hides, 
they  having  more  strength  than  the  hides  from  old  animals. 

"  Suitable  leather  having  been  chosen,  though  it  may  be  ever  so 
good,  may  be  spoiled  in  currying,  and  as  this  is  an  important  part, 
6 


82  RULES    FOR    BELTING. 

it  is  conducted  under  my  own  supervision,  where  I  have  the  shoulders 
cut  from  the  hides,  and  nothing  but  4  feet  in  length  of  the  choice  butts, 
curried  for  belting  purposes,  as  the  shoulder  naturally  stretching  in  a 
different  direction  from  the  butts,  causes  that  great  annoyance  in 
factories  of  belts  running  crooked. 

"  The  putting  on  of  belts  should  be  done  by  a  person  acquainted 
with  the  use  of  belting,  and  too  much  judgment  cannot  be  exercised 
in  this  respect,  as  the  wear  of  the  belt  depends  considerably  on  the 
manner  in  which  it  is  put  on,  therefore,  the  following  suggestions,  if 
practised,  will  be  of  much  service  to  persons  employed  in  this  capacity. 
The  butts  to  be  joined  together,  should  be  cut  perfectly  square  with 
the  belt,  in  order  that  one  side  of  the  band  may  not  be  drawn  tighter 
than  the  other.  For  the  joining  of  belts,  good  lace  leather,  if  prop- 
erly used,  being  soft  and  pliable,  will  always  give  better  satisfaction 
than  any  patent  fastening  or  hooks  which  have  yet  been  invented. 

"  Where  belts  run  vertically,  they  should  always  be  drawn  moder- 
ately tight,  or  the  weight  of  the  belt  will  not  allow  it  to  adhere  closely 
to  the  lower  pulley,  but  in  all  other  cases  they  should  be  slack. 

"  In  many  instances,  the  tearing  out  of  lace  holes  is  often  unjustly 
attributed  to  poor  belting,  when,  in  reality,  the  fault  lies  in  having  a 
belt  too  short,  and  trying  to  force  it  together  by  lacing,  and  the  more 
the  leather  has  been  stretched  while  being  manufactured,  the  more 
liable  it  is  to  be  complained  of. 

"All  leather  belting  should  occasionally  be  greased  with  the  fol- 
lowing mixture,  or  it  will  become  dry  and  will  not  adhere  to  the  pul- 
leys :  one  gallon  neat's-foot  or  tanners'  oil,  one  gallon  tallow,  twelve 
ounces  resin,  dissolved  by  heat,  and  well  mixed  together,  to  be  used 
cold,  th6  belt  having  been  previously  dampened  with  warm  water, 
except  where  it  is  spliced  together.  During  the  winter  season,  an 
extra  quantity  of  oil  should  be  added  to  the  mixture. 

"  To  obtain  the  greatest  amount  of  power  from  belts,  the  pulleys 
should  be  covered  with  leather ;  this  will  allow  the  belts  to  be  run  very 
slack,  and  give  25  per  cent,  more  wear.  I  drive  a  large  circular  saw, 
requiring  15  horse-power,  with  a  very  slack  belt,  the  pulleys  being 
covered  with  leather. 

"  For  heavy  counter  belts  not  intended  to  be  used  on  cone  pulleys, 
or  at  half  cross,  I  recommend  double  belts,  made  from  shoulders 
only,  which  I  furnish  at  the  price  of  single  belting ;  and  as  the  stretch 
is  taken  out  from  the  shoulders  after  they  are  cut  from  the  side,  they 
are  guaranteed  to  give  better  satisfaction  as  a  counter  belt  than  a 
single  belt  will. 


RULES    FOR    BELTING.  83 

"  More  power  can  be  obtained  from  using  the  grain  side  of  a  belt 
to  the  pulley  than  from  the  flesh  side,  as  the  belt  adheres  more  closely 
to  the  pulley ;  but  there  is  this  about  it,  the  belt  will  not  last  half  so 
long,  for  when  the  grain,  which  is  very  thin,  is  worn  off,  the  substance 
of  the  belt  is  gone,  and  it  then  quickly  gives  out ;  so  that  I  would 
advise  the  more  saving  plan  of  obtaining  power  by  driving  with  wider 
belts,  and  covering  the  pulleys  with  leather. 

"  Where  belts  are  to  run  in  very  damp  places,  or  exposed  to  the 
weather,  I  would  recommend  the  use  of  rubber  belting;  but  for  ordi- 
nary use  it  will  not  give  the  satisfaction  which  is  so  generally  ob- 
tained from  using  oak  leather  belting,  as  it  cannot  be  run  on  cone 
pulleys  through  forks,  or  at  half  cross,  and  with  fair  usage  would  be 
worn  out,  while  a  leather  belt  was  regularly  performing  the  work 
allotted  to  it ;  for  when  the  edge  becomes  worn,  the  belt  soon  gives  out." 

We  formularize  the  following  rules  from  the  text :  — 

HP.     SWcv 


16000 
16000  HP 


w= 


In  which  HP=  number  of  horse-power  transmitted. 
"  W=  width  of  belt  in  inches. 

"  c  =  belt  contact  with  smaller  pulley  in  lineal  feet. 

"  v  =  velocity  of  belt  in  feet  per  minute. 

The  following  examples  are  given:  "A  13|-inch  belt,  running  at 
the  rate  of  1600  Fpm,  over  a  4-feet  pulley,  and  touching  5  feet  of  its 
circumference,  gives  20  horse-power."  This  is  equal  to  88.888  square 
feet  of  belt  per  minute,  per  horse-power. 

"  A  20-inch  belt  at  2000  Fpm,  on  6  feet  of  the  circumference  of  a 
4-feet  pulley,  gives  45  horse-power."  This  is  equal  to  74.074  square 
feet  of  belt  per  minute  per  horse-power. 

To  Measure  Belts  in  Coil. 

64*  In  order  to  calculate  the  length  of  a  belt  in  coil,  we  may 
consider  the  coil  as  composed  of  a  series  of  concentric  circles,  and 
then  calculate  the  sum  of  their  circumferences  for  the  total  length 
of  the  coil ;  but  this  would  be  tedious,  and  a  simple  method  should 
be  devised. 

To  obtain  this,  first,  find  the  mean  diameter  of  the  extreme  coil 


84  RULES    FOR    BELTING. 

diameters  by  taking  half  the  sum  of  the  diameters  of  the  outer  and 
inner  coils,  multiply  this  number  by  3.1416,  and  then  by  the  number 
of  coils,  this  will  give  the  total  length  of  the  coil  in  inches  if  the 
diameters  of  the  coils  were  taken  in  inches. 
A  formula  expressing  this  rule  will  be : 

L  =  3.1416  n 

and  may  be  simplified  thus : 

L  =  1.5708  n(D  +  d). 

In  both  of  which  L  D  and  d  must  represent  like  units  of  measure- 
ment. 

To  simplify  calculations  still  further  by  getting  the  length  L  in 
feet,  and  the  diameters  D  and  d  in  inches,  the  rule  may  be  put  into 
this  form,  which  is  probably  the  best  for  use : 

L  =  .1309  n(D+  d). 

From  Appleton's  "American  Cyclopaedia"  we  take  the  following: 

65.  "  Belts  are  used  instead  of  gearing  when  the  shafts  to  be  con- 
nected are  far  apart. 

"  Belts  in  general  are  used  between  parallel  shafts,  and  when  the 
direction  of  motion  is  desired  to  be  reversed  the  belt  is  crossed. 

"  The  diameters  of  belt  pulleys  are  in  the  inverse  ratio  of  their 
speeds. 

"  To  modify  the  velocity  while  in  motion,  conical  drums  are  em- 
ployed on  parallel  shafts,  with  the  cones  reversed  in  position,  and  a 
shifter  used  to  move  the  belt,  and  hold  it  in  any  desired  position. 

"  When  shafts  are  not  parallel,  but  are  in  the  same  plane,  the  only 
way  to  connect  them  by  belts  is  to  use  a  third  shaft  placed  across 
both,  and  at  equal  angles,  or  nearly  so,  with  each,  and  to  which  each 
is  connected  by  a  belt. 

"  When  shafts  are  neither  parallel,  nor  in  the  same  plane,  they  -can 
be  connected  by  a  belt,  but  there  is  only  one  place  on  the  shafts  for 
the  pulleys.  These  must  be  at  the  ends  of  a  straight  line,  perpen- 
dicular at  the  same  time  to  both  axes.  There  is  only  one  such  line. 
This  theoretical  place  has  to  be  corrected  in  each  particular  case  ac- 
cording to  the  diameters  of  the  pulleys,  by  taking  care  that  the  belt 
arrives  square  on  each  pulley,  no  matter  how  obliquely  it  leaves  the 
other. 


RULES    FOR    BELTING.  85 

"As  a  consequence  of  this  unavoidable  connection,  the  motion  of 
the  shafts  cannot  be  reversed  without  securing  the  pulleys  in  other 
places. 

"  A  careful  attendant  will  make  a  belt  last  five  years,  which  through 
neglect  might  not  last  one. 

"  It  has  been  found  in  practice  that  belts  must  not  be  run  faster 
than  30  feet  per  second,  nor  have  a  tension  of  above  300  Ibs.  per 
square  inch  of  section. 

"  The  friction  of  a  belt  is  double  on  wood  what  it  is  on  cast  iron. 

"If  a  belt  is  passed  over  a  horizontal  cylinder  with  a  known  weight 
suspended  at  one  end,  and  a  spring  balance  attached  to  the  other, 
and  gradually  let  go  until  the  belt  begins  to  slide,  the  suspended 
weight,  minus  the  weight  indicated  by  the  balance,  is  the  friction. 

"It  has  been  found  that  by  taking  a  turn  and  a  half  around  a 
rough  cylindrical  post,  1  Ib.  will  hold  110  Ibs.  in  check,  and  that  by 
taking  2^  turns  1  Ib.  will  hold  2500  Ibs. 

"A  12-inch  belt  over  a  4-feet  pulley,  at  30  feet  per  second,  will 
transmit  the  power  of  a  6-inch  cylinder  engine  having  12-inch  stroke, 
running  125  Rpm,  under  60  Ibs.  of  steam." 

If  we  allow  30  Ibs.  average  pressure  per  square  inch  on  piston,  this 
engine  will  give  6-4  horse-power,  and  the  data  above,  281.25  square 
feet  of  belt  per  horse-power  per  minute,  which  is  a  liberal  allowance. 

Pulleys  with  Leather  Covering. 

66*  "  The  sliding  or  slipping  of  belts  on  the  pulleys  is  an  evil 
experienced  by  almost  every  one  whose  business  depends  on  machine 
power.  Various  means  have  been  devised  to  avoid  it.  One  of  them 
is  to  strew  powdered  rosin  or  pitch  on  the  inside  of  the  belt.  An- 
other is  to  cover  the  pulleys  with  wood.  A  third  is  to  give  the  rim 
of  the  pulley  a  curved  surface.  These  means  are  only  palliatives, 
and  lack  a  thorough,  steady,  and  continued  action.  Rosin  and  pitch 
are  soon  pressed  into  the  leather,  when  they  not  only  lose  their  effi- 
cacy, but  contribute  to  the  rotting  and  destruction  of  the  belts.  A 
wood  covering  on  the  pulley  gets  polished  in  a  short  time,  and  is 
then  as  slippery  as  iron.  It  is  therefore  necessary  to  frequently 
roughen  its  surface,  by  which  operation  the  diameter  of  the  pulley  is 
diminished,  and  the  proportions  of  the  transmission  are  altered.  A 
convexity  of  the  rim  of  the  pulley  is  very  effective  to  prevent  the 
dropping  off  of  the  belt,  especially  when  the  pulley  has  a  horizontal 
position ;  but  it  counteracts  the  slipping  of  the  belt  to  but  a  small 
extent. 


86  RULES    FOR    BELTING. 

"We  therefore  take  pleasure  in  communicating  to  the  public  a 
mechanical  contrivance,  which  completely  prevents  the  sliding  of 
belts,  and  all  the  great  disadvantages  resulting  from  it.  It  consists 
in  covering  with  leather  the  working  surface  of  the  pulleys.  As  the 
friction  of  leather  on  leather  is  equal  to  five  times  that  of  leather  on 
iron,  and  as  leather  can  be  roughened  and  be  easily  kept  in  that  con- 
dition, it  is  evident  that  a  sliding  of  the  belts  cannot  take  place  on 
pulleys  covered  with  leather,  not  even  when  the  belts  have  to  trans- 
mit the  very  highest  amount  of  power.  We  have  seen  such  pulleys 
working  in  sugar  factories,  breweries,  in  manufactories  of  German 
silver,  in  paper  mills,  machine  shops,  sawing  mills,  and  in  many  other 
mechanical  establishments,  in  all  of  which  they  have  proved  of  emi- 
nent usefulness  and  great  practical  value.  With  pulleys  which  have 
to  run  at  a  great  velocity,  as,  for  instance,  those  which  drive  blowers 
and  saw-frames,  as  well  as  with  pulleys  of  small  diameter,  which 
transmit  powerful  strains,  the  advantages  of  a  leather  covering  are 
especially  great.  But  besides  these  evident  advantages  resulting 
from  the  avoidance  of  the  slipping,  a  leather  covering  on  the  pulley 
preserves  the  belt,  in  the  first  place,  because  the  belt  does  not  require 
tightening  so  hard,  the  friction  being  considerably  increased  ;  and  in 
the  second  place,  because  there  is  no  occasion  for  a  rapid  rotting  of 
the  belt.  For  this  rapid  rotting  is  generally  caused  by  the  fact  that, 
under  the  influence  of  the  heat  produced  by  friction,  the  tannic  and 
sebacic  acids  contained  in  the  leather  of  the  belts  combine  chemically 
with  some  of  the  iron  of  the  pulleys,  forming  a  hard  compound  in 
the  belts,  which  produces  what  is  called  rottenness,  and  frequently 
causes  breakages.  This  evil  is,  of  course,  avoided  by  covering  the 

pulleys  with  leather.     . The  coverings  are 

fixed  to  the  pulleys  by  a  kind  of  paste  or  glue,  which  hardens  in  a 
very  short  time,  and  sticks  so  well  to  iron  and  leather,  that  the  great- 
est forces  can  be  transmitted  by  the  pulleys  without  loosening  the 
leather.  The  operation  of  covering  is  very  simple,  and  can  be  done 
and  renewed  by  every  intelligent  workman.  The  price  is  1|  Prus- 
sian thalers  per  square  foot  of  leather,  including  the  glue." — Trans- 
lated from  Polyt  Centralblatt.  From  Van  Nostrand's  Eclectic  Engi- 
neering Magazine,  July,  1869,  p.  604. 

From  a  "  Practical  Treatise  on  the  Manufacture  of  Worsteds  and 
Yarns,"  M.  Leroux,  H.  C.  Baird,  Philadelphia,  1869,  we  extract 
the  following : 

67.  "  It  is  rare  that  a  force  of  over  10  horse-power  is  transmitted 
by  means  of  belts. 


RULES    FOR    BELTING. 


87 


"  For  a  force  of  8  or  10  horse-power  the  belts  should  be  double, 
which  prevents  their  stretching ;  that  is  to  say,  two  belts  are  super- 
posed and  sewed  together  at  their  edges.  Thus,  for  a  9  horse-power 
two  belts  are  sewed  together,  one  of  which  is  1  millimetre  thicker 
than  the  other :  5.5  below  and  4.5  above,  making  10  millimetres,  the 
thickness  of  a  belt  which  will  resist  the  action  of  this  power  and 
even  a  greater  one.  For  low  powers  the  thickness  is  always  from  4 
to  5  millimetres. 

Table  fop  ascertaining  the  Width  of  Belts. 


VELOCITY 
PER  MINUTE 

IN 

METRES. 

WIDTH  OF  TANNED  LEATHER  BELTS  IN  MILLIMETRES. 
FORCE  IN  HORSE-POWER. 

A 

i\ 

A 

T9TF 

1 

2 

3 

20 
30 
40 
50 
60 
70 
80 
90 
100 
120 
140 
160 
180 
200 
240 
280 
300 
360 
400 
500 
600 
700 
800 
900 
1000 
1200 
1500 
2000 

68 
44 
34 
26 
22 
19 
17 
15 
13 
11 
9 
8 

132 
88 
66 
53 
44 
38 
33 
29 
26 
22 
19 
17 
15 
13 
11 
9 
8 

328 
220 
164 
132 
110 
94 
82 
73 
66 
55 
47 
41 
37 
33 
28 
24 
22 
18 
16 
13 

394 
296 
237 
197 
170 
148 
132 
119 
99 
85 
74 
66 
55 
47 
41 
39 
33 
28 
24 

220 
188 
165 
147 
132 
120 
94 
82 
73 
66 
55 
47 
44 
37 
33 
26 
22 

440 
377 
329 
293 
264 
220 
188 
165 
147 
132 
110 
94 
88 
73 
66 
53 
44 
38 

565 
494 
440 
396 
330 
283 
247 
220 
198 
165 
141 
132 
110 
99 
79 
66 
56 
50 
44 
40 
33 
26 
20 



"  The  transmission  of  motion  from  one  shaft  to  another,  by  means 
of  belts,  depends  entirely  upon  the  friction  produced  by  their  tension 


88  RULES    FOB    BELTING. 

upon  the  pulleys  or  drums  around  which  they  are  made  to  move.  If 
the  force  transmitted  by  them  is  augmented,  the  friction  is  in  like 
manner  increased ;  and,  if  in  that  case  the  tension  of  the  belts  remains 
the  same,  their  friction  surface,  or,  what  amounts  to  the  same,  their 
breadth  must  be  increased :  the  powers  to  be  transmitted  are  to  each 
other  as  the  product  of  the  width  of  the  belts  multiplied  by  the  velocity. 

"  M.  Morin  has  found  that  belts  of  tanned  leather  will  resist  a  ten- 
sion computed  at  2  kilogrammes  for  every  square  millimetre  of  their 
section. 

"  When  it  is  desired  to  determine  the  width  of  a  certain  belt,  mul- 
tiply the  number  of  revolutions  of  the  pulley  or  drum  made  in  one  minute 
by  its  circumference,  and  the  product  will  express  in  metres  the  desired 
velocity.  The  width  in  millimetres  will  then  be  found  opposite  this 
number  and  in  the  column  of  the  foregoing  table  of  the  given  power. 
If  pulleys,  however,  are  not  in  the  relation  of  identical  diameters,  but 
are  in  the  relations  about  to  be  mentioned,  then  multiply  the  width  given 
in  the  foregoing  table  by  the  coefficient  of  transformation. 

Coefficient  of  Transformation  of  the  Width  of  Belts  According  to 
the  Relations  of  the  Diameters  of  Pulleys. 

"  For  pulleys,  the  diameters  of  which  are  to  each  other  as  1  :  2, 
the  width  indicated  in  the  table  will  be  multiplied  by  0.75.  For 
the  ratio  of  1  :  3,  the  multiplier  will  be  0.65 ;  and  for  the  ratio  of 
1  :  4,  0.58." 

Experience  shows  that  belts  ought  never  to  be  less  than  20  milli- 
metres wide,  as  they  are  subject  to  stretching  and  breakage.  Their 
width  should  also  exceed  that  ascertained  from  the  table  by  at  least 
one-sixth.  Machines  working  different  materials,  with  varying  quan- 
tities, undergo  more  or  less  strain.  Thus,  a  spinning-mule,  after 
having  worked  ten  hours,  absorbs  i  more  power  than  at  the  outset. 
Wet  weather  occasions  the  same  effect,  while  obstructions,  want  of 
oiling,  materials  more  or  less  difficult  to  spin,  etc.,  are  so  many  causes 
which  have  to  be  neutralized  by  developing  the  friction  surface  of 
the  belts. 

Loss  of  Velocity  Suffered  by  Belts  while  in  Motion. 

The  variable  length  of  the  belts  has  an  influence  upon  their 
slipping.  When  they  are  crossed  they  are  less  liable  to  slip. 

"  The  loss  of  velocity  suffered  by  belts  when  mounted  depends  upon 
their  friction  surface. 

"  Long  belts  are  less  liable  to  slip  than  short  ones,  for  the  latter 


RULES    FOR    BELTING 


89 


are  always  stretched  in  a  manner  injurious  to  the  journals  and  brasses, 
and,  notwithstanding  this  amount  of  tension,  they  are  still  subject  to 
a  considerable  loss  in  velocity. 

"  I  have  undertaken  some  experiments  in  regard  to  losses  of  this 
nature  to  which  belts  are  liable  relatively  to  their  lengths,  and  I 
have  thought  it  well  to  prepare  a  table  for  calculating  the  amount 
of  motion  transmitted  by  belts  which  no  operator  can  well  do  without. 

Table  Showing  the  Slip  of  Leather  Belts  Relatively  to  their  Lengths. 


PARALLEL  BELTS. 

CROSSED  BELTS. 

Length  in  Metres. 

Percentage  of 
Velocity  Lost  by 
Slipping. 

Length  in  Metres. 

Percentage  of 
Velocity  Lost  by 
Slipping. 

2 

4.2 

2 

3.5 

4 

3.9 

4 

3.2 

6 

3.6 

6 

2.9 

8 

3.3 

8 

2.6 

10 

3.0 

10 

2.3 

12 

2.7 

12 

2.0 

14 

2.5 

14 

1.8 

16 

2.3 

16 

1.6 

18 

2.1 

18 

1.4 

20 

1.9 

20 

1.2 

"  Belts,  after  having  served  for  a  certain  length  of  time,  and  having 
withstood  more  or  less  tension,  become  greatly  impaired  by  stretching 
and  narrowing. 

"  The  width  of  belts  diminishes  in  proportion  to  the  strain  upon 
them.  Experience  shows  that  on  the  first  day  a  belt  is  used  it  suffers 
an  elongation  of  one  per  cent.  This  action  continues  to  diminish  till 
the  third  day,  after  which  the  belt  works  on  without  much  change 
in  its  dimensions. 

"  The  causes  producing  loss  of  velocity  in  belts  are,  imperfect  lubri- 
cation of  machinery,  obstructions  in  the  journal  boxes,  wheel  gearing 
out  of  line,  inferior  quality  of  leather,  couplings  and  sewing,  and  oil 
on  the  pulleys. 

"  When  a  belt  slips,  the  difficulty  is  remedied  by  sprinkling  the 
rubbing  surface  with  a  mixture  of  Spanish  white  and  resin.  If  the 
belt  is  smeared  with  oil,  Fuller's  earth  is  employed,  which  has  the 
property  of  absorbing  greasy  substances,  and  the  rubbing  side  of  the 
belt  is  then  scraped  with  a  wooden  blade. 


90  RULES    FOR    BELTING. 

"  Very  often  a  badly-made  knot  in  a  coupling  joint  will  cause  the 
belt  to  lose  1  or  2  per  cent,  of  velocity. 

"  To  transmit  and  secure  the  motion  to  be  imparted,  the  belts  are 
sewed  in  such  a  manner  as  best  to  insure  against  their  slipping ;  but 
as  they  always  tend  to  elongate,  in  order  to  obviate  this  difficulty,  the 
ends  are  bound  together  by  a  leather  thong.  These  are  generally  of 
Hungarian  leather,  cut  into  thin  and  narrow  strips,  so  as  to  be  readily 
handled,  as  well  as  to  avoid  the  necessity  of  punching  large  holes  in 
the  belt,  which  greatly  lessens  its  strength. 

"  The  flaxen  or  hempen  thread,  intended  for  sewing  belts,  ought 
to  be  of  superior  quality,  and  smeared  with  some  pitchy  substance  to 
prevent  ravelling. 

"  M.  Hunebelle,  of  Amiens,  manufactures  very  durable  belts,  the 
couplings  of  which  are  made  of  Hungarian  leather  prepared  in  some 
peculiar  manner.  I  have  substituted  animal  substances  for  thread. 
I  have  had  good  results  from  eel-skins,  and  have  also  tried  small 
cat-gut.  My  experience  has  been  that  the  belt  of  a  spinning-frame, 
sewed  with  this  material,  may  last  two  years  without  suffering  any 
deterioration  ;  and  the  cost  of  this  article  is  not  so  great  as  to  oblige 
us  to  reject  its  employment. 

"  Pulleys  should  have  a  rise  of  -fa  of  their  face  width. 

"  Sometimes,  to  impart  motion  to  a  machine  situated  at  a  distance 
from  the  transmission,  we  resort  to  what  is  called  a  binder  or  carrying 
pulley,  which  consists  of  two  small  wooden  drums,  having  a  face  con- 
vexity of  ^V  of  their  width,  secured  to  iron  axles  running  in  brasses, 
the  whole  made  adjustable.  These  drums  should  never  be  less  than 
20  centimetres  (Om.20)  in  diameter;  a  larger  diameter  never  does 
harm.  This  contrivance,  which  was  first  introduced  by  a  foreman 
named  Buignet,  stretches  the  belt  in  every  direction." 

Mr.  C.  R.  Rossman,  in  "Technologist"  for  Oct.,  1871,  suggests: 

68.  As  a  safe  working  tension  for  single  leather  belts  the  allow- 
ance of  45  Ibs.  to  the  inch  of  width,  and  adds  the  following : 

A  125-horse  engine  drives  two  18-inch  belts  over  8-feet  pulleys, 
making  75  Rpm.  This  gives  a  velocity  of  1875  Fpm,  and  a  tension 
of  61  Ibs.  to  the  inch  of  belt. 

"  This  is  in  excess  of  the  safe  limit  of  tension  generally  recom- 
mended ;  but  we  may  here  remark  that  belts  of  the  width  here  men- 
tioned are  generally  thicker  and  stronger  than  the  average  belts  used, 
and  from  which  the  ordinary  data  were  taken.  But,  from  a  careful 
examination  of  a  great  number  of  cases  of  belts  of  ordinary  width  and 


RULES    FOR    BELTING.  91 

strength,  we  find  that  a  safe  and  judicious  limit  lies  between  40  and 
50  Ibs.  In  order  to  increase  this,  however,  it  is  not  unusual  for  engi- 
neers to  double  the  thickness  of  the  belt  by  cementing  or  riveting  two 
thicknesses  of  leather  together.  But  this  plan,  though  advisable  in 
some  cases,  is  not  so  economical  of  power  and  material  as  the  equally 
efficient  plan  of  increasing  the  width  of  the  belt. 

"  The  tensile  strength  of  good  ox-hide,  well  tanned,  has  been  care- 
fully examined,  with  the  following  results : 

The  solid  leather  will  sustain,  per  inch  of  width,  675  Ibs. 

At  the  rivet  holes  of  the  splices,    "  "  382   " 

At  the  lacing,  "  "  210   " 

Safe  working  tension,  "  "  45   " 

"  The  belts  are  assumed  to  be  £  of  an  inch  thick." 

From  C.  F.  ScholPs  "  Mechanic's  Guide,"  pages  483-5. 

69.  "  Pulleys  must  be  true  and  concentric  and  their  shafts  par- 
allel, otherwise  belts  which  run  upon  them  must  be  guided,  and  the 
guiding  device  will  wear  their  edges  rapidly.  To  prevent  belts  from 
running  off,  pulleys  should  be  made  convex  on  their  faces,  much  con- 
vexity, however,  is  destructive  to  thick  and  to  double  belts.  Pulleys 
for  shifting  belts  should  be  parallel-faced,  except  where  the  shafts  are 
far  apart,  when  they  may  be  convex.  Flanges  to  pulleys  and  belt- 
guides  should  be  avoided,  except  to  pulleys  on  upright  shafts  which 
have  a  slower  motion,  and  where  two  belts  run  closely  together  on  the 
same  pulley,  or  on  two  pulleys  of  like  size ;  but  for  high  speed  they 
may  be  discarded. 

"The  softer  woods  are  better  for  pulleys  than  the  harder  kinds, 
but  pear-wood  and  nut-tree  are  best  for  cord-wheels.  Grease  must 
not  be  put  on  wooden  wheels  on  which  belts  run. 

"  Tighteners  must  be  applied  to  the  slack  side  of  belts. 

"  Good  oak-tanned  wild  leather  is  the  best  for  belts,  and  not  that 
prepared  with  alum. 

"  The  belts  should  be  cut  from  the  centre  of  the  skin,  stretched, 
and  of  even  thickness  throughout.  The  ends  are  joined  by  leather 
laces,  rove  through  uniformly-punched  holes. 

"  New  belts  are  liable  to  stretch,  and  should  be  unlaced,  shortened, 
new  holes  punched,  and  then  laced  again. 

"  The  most  practical  method  of  fastening  the  ends  of  belts  is  by 
the  screws  shown  in  Fig.  11.  The  belt  must  travel  in  the  direction, 
of  the  arrow,  and  never  allowed  to  run  against  the  joint. 


92 


RULES    FOB    BELTING. 


"  The  method  shown  in  Fig.  12  is  also  recommended.  The  plate 
is  of  brass,  rather  narrower  than  the  belt,  curved  to  the  pulley,  lap- 
ping the  joint,  and  receives  countersunk  head-screws  from  each  end  of 
the  belt. 


Fig,  11. 

"In  Fig.  13  another  plan  is  shown  in  which  incurved  teeth  of 
malleable  iron  connected  to  a  plate,  are  driven  through  each  end  of 
the  belt  when  butted,  and  are  then  clinched  on  the  inside. 


Fig.  12. 


Fig.  13. 


"  Thickness  of  belt  does  not  always  give  strength.  Small  pulleys 
injure  the  structure  of  the  belt  by  too  great  flexure.  Single  belts  are 
relatively  more  durable  than  compound  belts ;  the  latter  should  be 
used  only  on  large  diameter  of  pulleys.  Gum  belts  and  belts  of 
which  gum  forms  a  part,  are  preferable  in  damp  localities,  but  they 
should  not  be  shifted  much. 

"  Horizontal  running  belts  should  be  long ;  their  own  weight  doing 
the  required  work  without  excessive  tension,  but  is  limited  to  a  shaft 
distance  of  about  28  feet.  At  a  greater  distance  than  this,  especially 
at  high  speeds,  belts  sway  injuriously  from  side  to  side. 

"  Powdered  Colophonium  may  be  applied  to  a  slipping  belt. 

"Belts  driving  mills  at  high  speed  work  better  than  toothed 
wheels,  and  all  machines  subject  to  intermittent  motions,  or  liable  to 
sudden  stoppage,  should  be  driven  by  belts. 

"  Fat  should  be  applied  to  belts,  say  every  three  months  of  their 
use:  they  should  first  be  washed  with  lukewarm  water,  and  then 
have  leather  grease  well  rubbed  in. 


RULES    FOR    BELTING.  93 

"A  good  composition,  which  should  be  applied  warm,  consists  of: 

Lard  or  Tallow 1  part. 

Fish  Oil 4     " 

Colophonium 1     " 

Wood  Tar 1     " 

An  Engineer  of  considerable  Practical  Experience  with  Machinery 

replies : 
70.     Rule  for  horse-power  of  a  belt  — 

HP  x  26000  __ 
Vx  Cx6  = 

In  which  HP  =  horse-power. 

"  V  —  velocity  of  belt  in  feet. 

"  C  =  circumferential  contact  with  smaller  pulley  in  feet. 

"  W==  width  of  belt  in  inches. 

"  Single  belts  have  given  us  the  best  satisfaction,  taking  less  power 
to  drive  them,  and  adhering  to  the  pulleys  much  better,  and  do  not 
crack  in  bending. 

"  The  area  of  belt  contact  determines  its  driving  power. 

"  For  fastening  the  ends  we  consider  hooks  the  best  for  small  belts. 
For  large  belts  we  use  hooks,  with  the  addition  of  a  piece  of  leather 
riveted  over  the  lap. 

"  The  best  composition  for  preserving  belts  and  giving  them  adhe- 
sion, is  oil  with  a  small  quantity  of  rosin  in  it. 

"  Thin  belts  are  better  than  thick  ones. 

"  The  convexity  of  pulleys  should  be  the  least  possible,  not  over  | 
inch  to  the  foot  of  breadth." 

Another  Engineer  gives  the  following: 

TJ£.  "  To  find  the  number  of  horse-power  which  a  belt  will  trans- 
mit, multiply  the  number  of  square  inches  of  belt  contact  with  the 
pulley  by  the  velocity  of  the  belt  in  feet  per  minute,  and  divide  the 
product  by  64000." 

A  Skilful  Machinist,  of  much  Experience  with  Experimental 
Machinery,  says  : 

7£.  "  The  best  method  of  joining  belts  that  I  know  of  is  by  the 
ordinary  lacing.  The  holes  therefor  should  be  punched  about  f  of 
an  inch  apart,  or  as  near  that  as  the  equal  division  across  the  belt 


94  RULES    FOB    BELTING. 

will  allow,  and  for  wide  belts  2  rows  of  holes  should  be  punched,  in 
a  zigzag  direction,  commencing  with  the  lace  in  the  middle  of  the 
belt,  and  lacing  singly  to  each  edge,  returning  to  the  centre,  and 
securing  the  ends,  crossing  the  lace  on  the  outside  of  belt. 

"  I  have  found  this  plan  preferable  to  the  one  generally  adopted, 
that  is,  of  lacing  double  at  once  across  the  belt  finishing  at  one  edge, 
the  objection  to  which  is  in  the  loosening  of  the  ends  of  the  lace  and 
yielding  of  the  joint  at  one  edge,  which  will  crook  the  belt  and  render 
it  liable  to  lateral  running,  off  the  pulleys,  against  flanges,  into  gear 
perhaps,  and  may  permanently  stretch  the  belt  so  unevenly  as  to 
make  straight  running  again  matter  of  impossibility." 

Belts  for  Rolling-Mills. 

7*9.  "Nearly  all  rolling-mills  iii  Pittsburgh  are  driven  with  belts, 
from  20  inches  in  breadth  upwards ;  something  like  the  proportions 
may  be  guessed  at  from  the  following :  One  mill  has  a  pulley  26  feet 
diameter,  66-inch  face,  with  two  32-inch  belts  running  to  a  pulley 
overhead,  about  8  feet  diameter.  Another  is  25  feet  diameter,  45- 
inch  face.  Engines  with  such  wheels  and  belts  are  being  built  every 
day,  giving  great  satisfaction. 

"  The  question  of  driving  rolling-mills  with  belts  might  be  dwelt 
upon,  but  its  advantages  must  be  apparent  to  any  practical  man." — 
The  Engineer,  March  4,  1871. 

A  Large  Leather  Belt. 

74.  "  At  the  New  Jersey  Zinc  Co.'s  works  at  Newark,  N.  J.,  is 
a  quadruple  leather  belt  of  unusually  large  dimensions.  It  is  102 
feet  long,  4  feet  wide,  and  weighs  2200  Ibs.  The  outside  layer  con- 
sists of  2  widths,  the  second  and  fourth  layers  of  3  widths,  and  the 
third  layer  of  4  widths;  all  the  layers  being  riveted  and  glued 
together,  and  the  end  joints  of  the  pieces  forming  the  several  layers 
are  lapped  to  give  the  greatest  tensional  strength  to  the  whole. 

"  It  runs  on  an  engine  band  wheel  24  feet  diameter,  with  straight 
face  4  feet  wide,  of  smooth  turned  iron,  and  over  a  driven  pulley  on 
the  line  shaft  of  7  feet  diameter  having  similar  face,  the  centre  of 
which  lies  5  feet  above  the  engine  shaft. 

"  It  has  been  in  use  three  years,  is  doing  well  and  giving  no  trouble, 
even  when  doing  its  heaviest  work. 

"  The  engine  has  a  cylinder  of  28  inches  diameter  and  5  feet  stroke, 
makes  35  Rpm  under  70  Ibs.  of  steam  and  14  Ibs.  of  vacuum ;  esti- 
mated capacity  of  belt  250  horse-power,  velocity  3080.7  Fpm,  and 


RULES    FOB    BELTING.  95 

49.3  square  feet  of  belt  travelling  per  minute  per  horse-power."  — 
J.  M.  Hartman. 

Mr.  Benjamin  Clement,  M.  M.,  of  the  Calico  Print  Works,  Dover, 
N.  H.,  communicates  the  following  : 

7o.     "  For  estimating  the  horse-power  of  belts,  I  use  the  formulae 
of  Hoyt  Bros.,  of  New  York,  which  are  : 


In  which  W=  width  of  belt  in  inches. 

"        V=  velocity  of  belt  in  feet  per  minute. 
"     HP  ~  horse-power. 

"         S=  square  inches  of  belt  in  contact  with  smaller  pulley. 
F  =  length  of  belt  in  feet  in  contact  with  smaller  pulley. 

"  The  above  supposes  each  square  inch  of  belt  in  contact  to  raise 
-|  Ib.  one  foot  high  per  minute. 

"  All  other  things  being  equal,  the  area  of  contact  will  govern  the 
driving  power. 

"  Castor-oil  drainings  are  the  best  for  leather  belts. 

"  The  grain  side  in  all  cases  should  go  next  the  pulley. 

"  My  practice  is  to  give  -f%"  per  foot  of  breadth  for  the  convexity 
of  pulleys. 

"  For  covering  pulleys  I  use  a  mixture  of  three  pints  of  glue  made 
up  with  vinegar,  to  which  I  add  a  common  teacup  full  of  Venice 
turpentine. 

'*  We  have  at  these  works  an  18"  single  belt  driven  by  a  pair  of 
bevel  gears.  The  belt  pulleys  about  30  feet  between  centres,  6  feet 
in  diameter,  and  make  100  Rpm.  The  gears  are  2J-"  pitch,  7"  face, 
and  have  48  teeth  ;  the  driven  one  wooden  cogs.  According  to  the 
relative  wear  I  consider  them  well  balanced. 

"  We  have  a  double  leather  belt  18"  wide,  35  feet  between  centres 
of  pulleys;  the  driven  pulley  5  feet  10"  diameter,  running  116  Rpm, 
which  has  given  off  130  horse-power  by  actual  tests  with  indicator 
applied  to  the  engine. 

"This  is  a  belt  velocity  of  2,117  Fpm,  and  a  surface  velocity  of 
24.42  square  feet  of  belt  per  minute  per  horse-power." 


96 


RULES    FOR    BELTING. 


The  Largest  Belt  in  the  World. 

76.  "  Messrs.  J.  B.  Hoyt  &  Co.,  of  New  York,  exhibited  in  Ma- 
chinery Hall  a  double  belt  of  oak  tanned  leather,  186J  feet  long,  60 
inches  wide,  and  weighing  2212  Ibs. 

"  This  is  believed  to  be  capable  of  transmitting  600  horse-power, 
and  is  made  for  the  'Augustine'  Mill  of  Jessup  &  Moore,  paper 
manufacturers,  Wilmington,  Del." —  Polytechnic  Review,  Philada. 

A  Heavy  Belt. 

77.  "  Messrs.  P.  Jewell  &  Sons,  Hartford,  show  a  double  belt 
147<j  feet  long  and  36  inches  wide,  and  weighing  1130  Ibs.,  or  over 
2.57  Ibs.  per  square  foot.    This  is  claimed  to  be  the  heaviest  belt,  per 
surface,  in  the  Exhibition." —  Polytechnic  Review,  Philada. 

Example. 

78.  "At  Druid  Hill,  Baltimore,  Md.,  a  Babcock  and  Wilcox  engine 
turns  a  28-feet  pulley  fly-wheel,  lagged  with  wood,  52  Rpm,  carrying 
three  single  leather  belts,  each  16  inches  wide,  and  developing  500 
horse-power,  which  equals  a  belt  transmission  of  36.6  square  feet  per 
minute  per  horse-power;  velocity  of  belt,  4579  Fpm." — G.  H.  Babcock. 

Strength  of  Band-Saw  Blades.  From  "  Polytechnic  Review,"  Phila. 

79.  "  Test  of  the  strength  of  eight  specimens  of  Perrin's  Band- 
Saw  Blades,  with  brazed  joints,  by  Richards,  London  &  Kelly,  made 
on  Riehle  Bros.  Testing  Machine,  July  19,  1876 : 


No. 

Thickness. 

Width. 

Width  nearest 
^  inch. 

Breaking 
weight. 

Strength  per 
square  inch. 

1 

.0346 

1.05 

_ 

7 
~7T 

7600 

209,193  Ibs. 

2 

.0353 

.62 

- 

-g 

4000 

182,765   " 

3 

.0365 

.745 

6000 

220,649   " 

4 

.0337 

1.062 

. 

1 

3000 

83,823*  " 

5 

.0310 

.625 

-I 

2230 

115,090f" 

6 

.0310 

.490 

A 

2000 

131,060f  " 

7 

.0335 

.280 

32 

2000 

213,210   " 

8 

.0310 

.094 

32 

485 

16,430   " 

*  Broke  at  end  of  joint. 


f  Broke  across  centre  of  joint. 


"The  average  strength  of  the  unjoined  pieces  was  446  Ibs.  for  each 
Y^  inch  in  width,  and  the  strength  of  the  weakest  (which  were  the 
narrowest  also),  323  Ibs.;  while  the  average  strength  through  the 


RULES    FOB    BELTING.  97 

joints  for  each  T^  inch  in  width  was  206  Ibs.  per  ^  inch ;  in  the 
weakest,  176  Ibs.  All  the  blades  for  the  ordinary  saws  are  made  of 
No.  19  B.  W.  G.  steel,  and  vary  only  by  the  inequalities  caused  by 
grinding  or  filing  the  joints.  The  knowledge  that  when  a  band-saw 
is  being  strained  to  the  amount  of  175  Ibs.  for  each  TJg  inch  in  width 
is  strained  to  nearly  its  limit  of  endurance,  may  be  of  some  value  to 
the  makers  and  users  of  band-saws." —  John  E.  Sweet. 

From  Dr.  H.  M.  Howe,  Franklin  Sugar  Refinery,  Philadelphia : 

80 '•  "  A  24-inch  diameter  iron  cylinder,  nearly  horizontal,  has  a 
stream  of  bone-black  running  constantly  through  it  at  a  temperature 
of  350°  Fah.  This  is  caused  to  revolve  by  a  7-inch  wide  gum  belt, 
applied  directly  to  the  naked  cylinder,  and  lasted  just  three  mouths. 
The  cylinder  was  used  20  to  22  hours  in  the  24.  Before  applying 
the  next  belt  the  cylinder  was  lagged  with  wood  1  inch  thick ;  two 
months  of  use  showed  no  appreciable  deterioration  of  the  belt. 

"  In  our  refinery  gum  belts  do  better  than  leather  in  hot  and  in 
damp  situations,  and  in  places  where  they  are  subjected  to  the  com- 
bined influence  of  heat  and  moisture. 

"  Single  leather  belts  seem  to  be  more  economical  than  double  ones 
in  places  where  the  atmosphere  is  charged  with  sugar  and  bone-black 
dust.  Double  belts  stiffen  and  crack,  then  the  pores  become  filled, 
and  dubbing  does  not  relieve  them,  but  forms  with  the  dust  a  glazing 
on  the  surface. 

"  Single  belts  are  not  likely  to  become  so  unpliable,  and  therefore 
hug  the  pulleys  better,  and  work  more  than  half  as  long  as  double 
belts.  Gum  belts  make  better  elevators  than  double  leather  belts. 

"Our  belts  are  generally  put  flesh  side  next  the  pulley;  have  had 
some  put  hair  side  next  the  pulley,  which  we  prefer,  believing  the 
adhesion  is  greater,  and  have  not  observed  any  less  liability  to  crack 
when  so  used. 

"In  our  'Mill  Room,'  where  there  is  much  sugar  dust,  but  no  great 
heat,  if  we  keep  the  belts  dry,  they  work  and  last  well ;  while  in  the 
'  Black '  rooms,  where  there  is  high  heat  and  dust  combined,  belts 
are  short  lived." 

The  Value  of  Rubber,  Gutta-percha,  and  Canvas  Belts 

as  compared  with  Leather. 

81.     "  Under  the  same  circumstances,  and  on  the  same  machines, 
these  bands  will  not  last  or  wear  one-fourth  as  long  as  leather.     When 
once  they  begin  to  give  out,  it  is  next  to  impossible  to  repair  them. 
7 


98  RULES    FOR    BELTING. 

"  Wide  bands  cannot  be  used  for  or  cut  up  into  narrow  ones,  as 
leather  can  be. 

"  Leather  belts  may  be  used  over  and  over  again,  and,  when  of  no 
further  value  for  belts,  can  be  sold  for  other  purposes. 

"A  rubber  baud,  costing  hundreds  of  dollars,  may  be  spoiled  in  a 
few  moments,  by  the  lacing  giving  out  and  the  band  being  run  off  into 
the  gearing,  or  by  being  caught  in  any  manner  so  as  to  damage  the 
edge,  or  by  stoppage  of  either  the  driving  or  driven  pulley.  A  few 
moments  of  quick  motion  or  friction  will  roll  off  the  gum  from  the 
canvas  in  such  quantities  as  to  spoil  the  band. 

"  Leather  belts  may  be  torn  or  damaged,  yet  are  easily  repaired. 

"  Should  a  rubber  or  gum  belt  begin  to  tear  by  being  caught  in  the 
machinery,  if  the  rent  strikes  the  seam,  it  is  most  certain  to  follow  it, 
even  the  entire  length,  if  the  machinery  is  not  stopped.  It  would  be 
impossible  to  tear  leather  in  like  manner. 

"  Oil,  in  contact  with  rubber  belting,  will  soften  the  gum. 

"  Rubber,  gutta-percha,  and  canvas  belts  will  continue  to  stretch  as 
long  as  in  use,  rendering  it  necessary  to  shorten  them  continually. 

"  During  freezing  weather,  if  moisture  or  water  finds  its  way  into 
the  seams,  or  between  the  different  layers  of  canvas  composing  these 
bands,  and  becomes  frozen,  the  layers  are  torn  apart,  and  the  band  is 
spoiled ;  or,  if  a  pulley  becomes  frosty,  the  parts  of  band  in  contact 
with  it  will  be  torn  off  from  the  canvas  and  left  on  the  pulley. 

"  Gum  belts  will  not  answer  for  '  cross '  or  '  half-cross '  belts,  for 
'  shifting '  belts, '  cone  pulleys,'  or  for  any  place  where  belts  are  liable 
to  slip,  as  friction  destroys  them.  .  .  . 

"  A  well-made  leather  band,  if  properly  looked  after  —  the  width 
and  pulley  surface  proportional  to  the  amount  of  work  to  be  done  — 
will  last  12,  15,  or  20  years,  and  yet  be  of  value  to  work  over  into 
narrow  belts." — J.  B.  Hoyt  &  Co. 

From  "Rankine's  Manual  of  Machinery  and  Mill  Work" 
we  take  the  following : 

82>  "  The  flexible  pieces  used  in  machinery  may  be  classed  under 
three  heads :  Cords,  which  approximate  to  a  round  form  in  section ; 
Belts,  which  are  flat ;  and  Chains,  which  consist  of  a  series  of  rigid 
links,  so  connected  together  that  the  chain,  as  a  whole,  is  flexible.  Mr. 
Willis  gives  them  all  the  common  name  of  wrapping  connectors,  and, 
for  the  sake  of  brevity  in  stating  principles  that  apply  to  them  all, 
they  may  conveniently  be  called  bands. 

"  The  effective  radius  of  a  pulley  is  equal  to  the  radius  of  the  pulley 
added  to  half  the  thickness  of  the  band. 


KULES    FOR    BELTING.  99 

"  Smooth  bands,  such  as  belts  and  cords,  are  not  suited  to  commu- 
nicate a  velocity-ratio  ivith  precision,  as  teeth  are,  because  of  their 
being  free  to  slip  on  the  pulleys ;  but  the  freedom  to  slip  is  advan- 
tageous in  swift  and  powerful  machinery,  because  of  its  preventing 
the  shocks  which  take  place  when  mechanism  which  is  at  rest  is  sud- 
denly thrown  into  gear,  or  put  in  connection  with  the  prime  mover. 
A  band  at  a  certain  tension  is  not  capable  of  exerting  more  than  a 
certain  definite  force  upon  a  pulley  over  which  it  passes,  and  there- 
fore occupies,  in  communicating  its  own  speed  to  the  rim  of  that 
pulley,  a  certain  definite  time,  depending  on  the  masses  that  are  set 
in  motion  along  with  the  pulley  and  the  speed  to  be  impressed  upon 
them,  and  until  that  time  has  elapsed  the  band  has  a  slipping  motion 
on  the  pulley ;  thus  avoiding  shocks,  which  consist  in  the  too  rapid 
communication  of  changes  of  speed. 

"  The  swell  usually  allowed  in  the  rims  of  pulleys  is  one  twenty- 
fourth  part  of  the  breadth." 

In  quarter  twist  belts,  "  in  order  that  the  belt  may  remain  on  the 
pulleys,  the  central  plane  of  each  pulley  must  pass  through  the  point  of 
delivery  of  the  other  pulley.  It  is  easy  to  see  that  this  arrangement 
does  not  admit  of  reversed  motion. 

"  The  safe  working  tension  of  leather  belts,  according  to  Morin,  is 
285  Ibs.  on  the  square  inch.  The  ordinary  thickness  of  belting  leather 
is  about  .16-inch. 

"  The  inside  of  the  leather  is  rougher  than  the  outside,  and  is  placed 
next  the  pulleys,  crossed  belts  being  twisted  so  as  to  bring  the  same 
side  of  the  leather  in  contact  with  both  pulleys. 

"  Leather  belts,  when  new,  are  not  quite  of  the  heaviness  of  water, 
say  60  Ibs.  per  cubic  foot ;  but,  after  having  been  for  some  time  in 
use,  they  become  thinner  and  denser  by  compression,  and  are  then 
about  as  heavy  as  water.  The  weight  of  single  belting  is  approxi- 
mately .068  Ibs.  per  one  inch  breadth  and  one  foot  length. 

"  Raw-hide  belts  have  a  tenacity  about  one  and  a  half  that  of  tanned 
leather.  When  raw  hide  is  used  for  belts  or  for  ropes  it  is  soaked 
with  grease,  to  keep  it  pliable  and  protect  it  against  the  action  of  air 
and  moisture. 

"  Gutta-percha  is  sometimes  used  for  flat  belts.  They  are  made  of 
the  same  dimensions  with  leather  belts  for  transmitting  the  same  force, 
and  are  nearly  of  the  same  weight. 

"  Woven  belts  are  made  of  a  flaxen  or  cotton  fabric,  a  sufficient 
number  of  plies  being  used  to  give  a  thickness  equal  to  that  of  leather 
belts,  and  cemented  together  with  india-rubber.  When  made  of  flax, 


100  RULES    FOR    BELTING. 

they  are  said  to  be  about  three  times  more  tenacious  than  tanned 
leather  belts  of  the  same  transverse  dimensions. 

"  Ultimate  tenacity  of  leather  rope,  10,000  feet,  or  3360  Ibs.  on 
the  circular  inch ;  of  raw  hide,  15,000  feet  and  5040  Ibs.  on  the 
circular  inch ;  safe  working  tension,  one-sixth  of  these  dimensions. 

"  The  ordinary  speed  of  wire  ropes  in  Mr.  C.  F.  Hirn's  '  Telody- 
namic  Transmission '  of  power  is  from  50  to  80  feet  per  second,  and 
with  wrought-iron  pulleys  it  is  considered  that  it  might  be  increased 
to  100  feet  per  second. 

"  In  order  that  the  rope  may  not  be  overstrained  by  the  bending 
of  the  wires  of  which  it  consists,  in  passing  round  the  driving  and 
following  pulleys,  the  diameter  of  each  of  those  pulleys  should  not  be 
less  than  140  times  the  diameter  of  the  rope,  and  is  sometimes  as  much 
as  260  times. 

"  The  distance  between  the  driving  and  following  pulleys  is  not 
made  less  than  about  100  feet,  for  at  less  distances  shafting  is  more 
efficient ;  nor  is  it  made  more  than  500  feet  in  one  span,  because  of 
the  great  length  of  the  catenary  curves  in  which  the  rope  hangs. 
When  the  distance  between  the  driving  and  following  pulleys  exceeds 
500  feet,  the  rope  is  supported  at  intermediate  points  by  pairs  of 
bearing  pulleys,  so  as  to  divide  the  whole  distance  into  intervals  of 
500  feet  or  less. 

"  The  bearing  pulleys  have  half  the  diameter,  and  are  of  similar 
construction  with  the  driving  pulleys. 

"  The  loss  of  work  due  to  the  stiffness  of  the  rope  may  be  regarded 
as  insensible ;  because,  when  the  diameters  of  the  pulleys  are  suffi- 
cient, the  wires  of  which  the  rope  is  made  straighten  themselves  by 
their  own  elasticity,  after  having  been  bent. 

"  Experience  shows  the  loss  of  power  by  the  axle  friction  of  driving 
and  following  pulleys  to  be  about  4^,  and  of  the  axle  friction  of  each 
pair  of  bearing  pulleys  about  ^0  of  the  whole  power  transmitted." 

Belts. 

"  The  driving  pulleys  fixed  upon  the  shaft  should  be  well  centred, 
so  that  there  may  be  no  inequality  of  motion  which  would  destroy 
the  belts. 

"  To  transmit  motion  to  the  apparatus  without  noise  or  loss  of  power, 
tanned  leather  belts  of  first  quality  are  preferably  used.  They  wear  one 
and  a  half  times  as  long  as  those  of  inferior  qualities,  which,  although 
their  low  price  is  an  inducement  to  purchasers,  are  more  expensive  in 
the  end,  by  the  stretching  and  rapid  deterioration  they  undergo. 


RULES    FOR    BELTING 


101 


"  The  greater  or  less  thickness  of  belts  often  contributes  to  their 
stretching,  and  the  continual  variations  to  which  they  are  subject 
while  extended  over  the  circumference  of  pulleys  or  drums. 

"  For  high  powers,  well  tanned  leather  of  sufficient  thickness  should 
be  preferred.  I  have  prepared  the  following  table,  which  gives  the 
thicknesses  of  belts  calculated  from  the  variable  power  of  machinery, 
and  the  diameters  of  pulleys : 


No.  OP 
HORSE-POWER. 

THICKNESS  IN  MILLIMETRES. 
PULLEY  DIAM.  AT  LEAST  =  Om  .30. 

THICKNESS  IN  MILLIMETRES. 
PULLEY  DIAM.  AT  LEAST  =  Om  .20. 

, 

« 

5 

1 

6* 

64 

2 

64 

6 

3 

7 

64 

4 

74 

7 

5 

8 

74 

6 

84 

8 

7 

9^ 

gi 

8 

9i  doubled  belt. 

9* 

doubled  belt. 

9 

10 

94 

"          " 

0 

11 

10 

" 

Extracts  from  paper  "On  the  Centrifugal  Force  of  Bands  in 
Machinery,"  by  W.  J.  M.  Rankine,  in  "  Engineer,"  March  5, 
1869. 

83.  "  It  is  well  known,  through  practical  experience,  that  a  belt 
for  communicating  motion  between  two  pulleys  requires  a  greater 
tension  to  prevent  it  from  slipping  when  it  runs  at  a  high  than  at  a 
low  speed. 

"  Various  suppositions  have  been  made  to  account  for  this,  such  as 
that  of  the  adhesion  to  the  belt  of  a  layer  of  air,  which  at  a  very 
high  speed  has  not  time  to  escape  from  between  the  belt  and  the 
pulley.  But  the  real  cause  is  simply  the  centrifugal  force  of  the 
belt,  which  acts  against  its  tension,  and  therefore  slackens  its  grip  of 
the  pulleys. 

.  .  .  "  It  can  be  proved  from  the  elementary  laws  of  dynamics, 
that  if  an  endless  band,  of  any  figure  whatsoever,  runs  at  a  given 
speed,  the  centrifugal  force  produces  an  uniform  tension  at  each  cross 
section  of  the  band,  equal  to  the  weight  of  a  piece  of  the  band,  whose 
length  is  twice  the  height  from  which  a  heavy  body  must  fall,  in 
order  to  acquire  the  velocity  of  the  band. 

"  In  symbols,  let  w  be  the  weight  of  a  unit  of  length  of  the  band ; 


102  KULES    FOR    BELTING. 

v  the  speed  at  which  it  runs,  and  g  the  velocity  produced  by  gravity 
in  a  second  (=  32.2  feet)  ;  then  the  centrifugal  tendon  (as  it  may  be 

called)  has  the  following  value  :  -  —  . 

y 

"  The  effect  on  the  band  when  in  motion  is,  that  at  any  given  point, 
the  tension  which  produces  pressure  and  friction  on  the  pulleys,  or 
available  tension  (as  it  is  called),  is  less  than  the  total  tension  by  an 
amount  equal  to  the  centrifugal  tension  ;  for  this  amount  is  employed 
in  compelling  the  particles  of  the  band  to  circulate  in  a  closed  or 
endless  path.  It  is,  of  course,  to  the  total  tension  that  the  strength 
of  the  band  is  to  be  adapted,  therefore  the  transverse  dimensions  of 
a  band  for  transmitting  a  given  force  must  be  greater  for  a  high  than 
for  a  low  speed. 

"  One  of  the  most  convenient  ways  of  expressing  the  size  of  a  band 
is  by  stating  its  weight  per  unit  of  length  ;  for  example,  in  pounds 
per  running  foot  or  in  kilogrammes  per  metre.  When  the  size  is 
expressed  thus,  the  corresponding  way  of  expressing  the  intensity  of 
any  stress  on  the  band  is  in  lineal  units  of  itself,  such  as  feet  or 
metres.  Let  b  denote  the  greatest  safe  working  tension  on  a  band  of 
a  given  kind,  in  units  of  its  own  length  ;  w,  as  before,  the  weight 
of  a  unit  of  length  ;  so  that  w  I  is  the  amount  of  the  safe  working 
tension  in  units  of  weight.  Let  T  be  the  amount  of  the  available 
tension  required  at  the  driving  side  of  the  band  for  the  transmission 
of  power,  being  usually  from  two  to  two  and  a  half  times  the  force 
to  be  transmitted.  Then  the  total  tension  is 


9    ' 

"  Whence  it  is  obvious  that  the  required  weight  per  unit  of  length 
is  given  by  the  following  formula  : 


"  For  example,  suppose  that  the  band  is  a  wire  rope,  that  the 
greatest  working  tension  is  to  be  equivalent  to  the  weight  of  2900 
feet  of  the  rope,  and  that  it  is  to  run  at  100  feet  per  second :  then 
we  have 

I  =  2900  feet; 

—  =  310  feet; 


RULES    FOR    BELTING.  103 

"And  consequently  the  weight  per  running  foot  of  the  rope  required 

is: 

w==          T T_ 

~  2900  —  310  ~  2590 ' 

"  Or  about  one-eighth  part  heavier  than  the  rope  required,  for  a 
speed  so  moderate  as  to  make  the  centrifugal  tension  unimportant. 

"  In  fixing  the  value  of  the  greatest  working  tension  on  a  wire 
rope,  a  proper  deduction  must  of  course  be  made  for  the  stress  pro- 
duced by  the  bending  of  the  wires  round  the  pulleys. 

"  That  stress  is  given  in  equivalent  length  of  rope  by  the  expression 

— ,  where  D  is  the  diameter  of  the  smallest  pulley  round  which  the 

rope  passes,  d  the  diameter  of  the  wire  of  which  the  rope  is  made, 
and  L  the  modulus  of  elasticity  of  the  wire,  in  length  of  itself,  viz. : 
about  8,000,000  feet,  or  2,400,000  metres.  That  is  to  say,  let  I,  be 
length  of  the  rope  equivalent  to  the  greatest  safe  working  tension 
on  a  straight  rope ;  I  as  before,  the  length  equivalent  to  the  actual 
greatest  working  tension,  then 


"  In  the  case  of  leathern  belts,  b  may  be  estimated  at  about  660 
feet,  or  200  metres. 

"  In  the  case  of  a  leather  belt  running  at  the  rate  of  100  feet  per 
second,  the  weight  per  unit  of  length  required,  in  order  to  exert  a 

t.     f       660  660 

given  available  tension,  is  increased  in  the  ratio  or  — — — —  ==——•» 

ooO  — -  olO        ooO 

or  to  nearly  double,  as  compared  with  that  of  a  belt  whose  centrif- 
ugal force  is  unimportant. 

"  The  sectional  area  of  a  leathern  belt  may  be  calculated  approxi- 
mately in  square  inches  by  multiplying  the  weight  per  running  foot 
by  2.3 ;  or  in  square  millimetres,  by  multiplying  the  weight  in  kilo- 
grammes to  the  running  metre  by  1000. 

"  The  ordinary  thickness  of  a  single  belt  being  about  0.16  inch,  or 
4  millimetres,  the  breadth  may  be  deduced  from  the  sectional  area 
by  dividing  by  that  thickness. 

"The  length  (L)  equivalent  to  the  modulus  of  elasticity  of  a  leath- 
ern belt,  as  calculated  from  Bevan's  experiments,  is  about  23,000 
feet,  or  7000  metres." 


104  RULES    FOR    BELTING. 

The  Sliding  of  Belts  and  its  Prevention. 

84:*  "  The  Praktisehe  Maschinen  Constriicteur  affords  us  an  excel- 
lent paper  upon  the  above  topic,  the  translation  of  which  reads  as 
follows : 

"  The  most  convenient  and  least  expensive  mode  of  transmitting 
power  consists,  undoubtedly,  in  the  use  of  belts.  Nevertheless,  this 
system,  owing  to  the  sliding  of  the  belts,  is  connected  with  a  great 
loss  of  power  that  is  seldom  observed.  Let  us  suppose  two  corre- 
sponding -pulleys,  of  the  same  diameter,  in  motion  at  a  moderate 
velocity.  In  case  the  tension  of  the  belt  is  sufficiently  great,  and 
the  pulleys  not  too  small,  it  may  be  difficult  at  first  to  perceive  the 
sliding  of  the  belt ;  but  if  the  rotations  of  both  the  pulley  and  the 
belt  are  counted,  a  difference  in  their  number  will,  in  nearly  all 
cases,  be  discovered,  the  belt  performing  a  less  number  of  rotations 
than  the  pulley.  We  thus  become  aware  that  the  belt  slides  upon 
the  smooth  surface  of  the  pulley,  owing  to  the  fact  that  the  power 
sought  to  be  transmitted  by  the  belt  is  greater  than  the  friction  of 
the  leather  upon  the  iron,  and  that  this  power  overcomes  the  friction, 
more  or  less  slowly,  according  to  the  circumstances  of  the  case.  In 
regard  to  this,  it  is  self-evident  that  the  velocity  and  diameter  of  the 
pulleys  must  be  taken  into  account,  for  the  friction  is  more  easily 
surmounted  at  a  rapid  velocity  than  at  a  slow  one,  and  pulleys  of 
large  diameter  offer  to  the  strap  more  surface,  and  this  increases  the 
friction.  The  consequent  sliding  of  the  straps  takes  place  the  more 
easily  the  greater  the  peripherical  velocity  and  the  power  to  be  trans- 
mitted, on  the  one  hand,  and  the  smaller  the  diameter  and  the 
breadth  of  the  driver  or  pulley  on  the  other. 

"  The  sliding  of  the  belt,  however,  represents  a  loss  of  power  and 
fuel.  Supposing  that  the  two  corresponding  pulleys,  of  equal  diam- 
eter, the  turning  one  makes  100  rotations  in  a  minute,  and  the  turned 
one  95,  there  will  be  a  loss  of  nearly  5  per  cent,  of  the  amount  of 
force  generated  by  the  motor. 

"It  will  become  clear  why  the  loss  amounts  to  not  quite  5  per 
cent,  when  it  is  taken  into  consideration  that  in  sliding  there  will  be 
a  surplus  of  the  transmitted  force  over  the  frictional  resistance  of  the 
belt,  which  will  be  expended  in  the  removal  of  the  friction.  This 
may  be  most  easily  recognized  when  we  have  a  very  considerable 
transmission  of  power,  and  when  a  perceptible  sliding  occurs,  as,  for 
instance,  in  driving  a  hydraulic  press.  If  the  pressure  upon  the  pis- 
ton of  the  pump  is  much  greater  than  the  friction  of  the  belt  upon 


RULES    FOR    BELTING.  105 

the  drum,  the  former  is  stopped  in  its  motion,  while  the  belt  runs 
around  the  driving  pulley,  the  motor  itself  thereby  attains  an  accel- 
erated velocity,  from  which  it  follows  that  the  force  required  to  over- 
come the  friction  is  less  than  the  one  necessary  for  the  working  of 
the  hydraulic  press. 

"  In  order  to  ascertain  this  loss  of  power  for  all  cases,  numerous 
and  extensive  experiments  had  to  be  undertaken.  It  may  be  stated 
here  that  this  loss  may  amount  to  as  much  as  20  per  cent.,  according 
to  the  circumstances.  It  may  appear,  at  first,  that  the  best  means 
of  guarding  against  this  loss  would  be  to  construct  the  pulleys,  in 
regard  to  diameter  and  width,  so  that  the  resistance  of  friction  could 
not  be  overcome  by  the  power  transmitted.  Nevertheless,  upon  a 
closer  examination,  it  will  become  evident  that  this  can,  in  most 
instances,  only  be  accomplished  at  great  expense.  The  outlay  for 
leather  belts  is  already  considerable  in  an  establishment  of  medium 
size,  and  would  be  still  greater  if  all  the  belts  were  to  be  taken  of 
such  a  width  as  is  necessary  for  the  prevention  of  sliding.  Other 
means  have,  therefore,  been  proposed  and  applied.  For  instance,  an 
endeavor  was  made  to  increase  the  friction  of  the  leather  upon  the 
iron  by  spreading  pulverized  rosin  or  asphaltum  upon  the  belt.  In 
instances  where  the  latter  ceases  to  draw,  the  effect  shows  itself  at 
once :  but,  nevertheless,  only  for  a  short  time.  On  account  of  the 
pressure,  the  resinous  powder  penetrates  the  belt,  so  that  its  surface 
soon  becomes  as  smooth  as  before,  while  the  leather  soon  gets  brittle 
and  is  gradually  destroyed. 

"  The  covering  of  the  pulleys  with  wood  is  less  objectionable,  but 
it  can  find  only  a  limited  application.  Only  a  wide  pulley  can  be 
lined  in  this  manner ;  but  as  the  wood  soon  gets  as  smooth  as  the 
iron,  it  is  necessary  to  roughen  its  surfaces  repeatedly.  This  brings 
about  a  change  in  the  diameter  of  the  pulley,  as  well  as  in  the 
amount  of  force  transmitted. 

"A  third  preventive,  which  seems  to  have  found  extended  appli- 
cation, consists  in  giving  to  the  pulley  a  convex  surface.  But  whe- 
ther this  prevents  the  belt  from  running  off  is  yet  to  be  proven.  The 
writer  has  ascertained  that  in  consequence  of  the  convexity  of  the 
drums,  the  belts  will  be  stretched  more  in  the  centre  than  at  the 
edges,  and  that  as  the  frictional  surface  thus  becomes  smaller,  the 

O        * 

danger  of  sliding  is  increased. 

"The  covering  of  the  pulleys  with  leather  is  undoubtedly  the  more 
advantageous,  as  thereby  the  frictional  resistance  is  increased ;  the 
co-efficient  of  friction  of  which,  with  the  leather,  is  considerably 


106  RULES    FOR    BELTING. 

greater  than  that  of  the  leather  upon  iron.     The  latter  amounts  to 
0.25,  the  former  to  1.25,  which  is  just  five  times  more. 

"  The  resistance  of  friction  may,  nevertheless,  be  greatly  increased 
by  roughening  the  leather  lining,  and  keeping  it  thus  by  means  of 
an  alum  or  salt  solution.  The  great  benefit  to  be  derived  from  this 
system  has  been  demonstrated  by  practical  tests. 

"  We  give  some  of  the  results  of  the  new  system.  A  spinning- 
machine  was  made  to  produce,  continually,  a  uniform  thread,  while 
by  the  sliding  of  the  belt  it  produced  a  thread  containing  knots  and 
unequal  spots.  Ventilators  which  made  only  1100  rotations  per 
minute,  in  consequence  of  sliding,  made  1400  after  sliding  was  pre- 
vented. In  a  steam-mill,  with  five  run  of  mill-stones,  each  set  ground 
27  bushels  per  day  after  the  pulleys  were  covered  with  leather,  while 
before  the  amount  ground  per  day  was  only  from  23  to  24  bushels. 
Moreover,  the  troublesome  falling  off  of  belts,  which  previously 
occurred  very  often,  ceased  altogether.  In  a  paper-mill,  a  rag  engine 
did  15  per  cent,  more  work  per  day  after  its  pulleys  were  covered 
with  leather.  In  sugar-mills,  for  the  beet  crushers  the  centrifugal 
and  other  apparatus,  this  system  has  been  fully  approved,  and  it  can- 
not be  doubted  that  it  will  be  of  advantage  wherever  introduced.  It 
may  be  remembered  that  leather  may  also  be  used  in  establishments 
where  the  power  is  transmitted  by  wire-ropes.  It  is  in  such  cases 
preferable  to  wood,  cork,  asphaltum,  and  gum. 

*'  The  reason  why  the  belts  last  longer  is  to  be  attributed  to  the 
fact  that  the  increased  friction  allows  a  lesser  degree  of  tension  of 
the  belts  than  would  be  the  case  if  they  were  to  run  on  a  smooth 
iron  surface.  It  is  well  known  to  every  machinist,  that  for  great 
transmissions  of  power  the  belts,  if  running  on  an  iron  surface,  must 
be  stretched  to  the  utmost  limit.  This  may  be  regarded  as  one  of 
the  causes  of  the  rapid  destruction  of  the  leather. 

"  The  same  result  is  brought  about  sooner  from  the  circumstance 
that,  on  account  of  the  friction,  fine  particles  of  iron  are  detached, 
which,  by  combining  with  the  tannic-acid  and  the  fatty  acids  in  the 
leather,  form  compounds,  which,  by  penetrating  the  leather,  cause 
the  same  to  become  brittle.  By  covering  the  pulleys  with  leather, 
this  evil  is  prevented.  But  the  chief  cause  of  the  rapid  destruction 
of  the  leather  is  to  be  attributed  to  the  sliding  itself,  which,  as  before 
mentioned,  represents  a  useless  loss  of  power.  By  the  friction  of  the 
leather  upon  the  iron  heat  is  generated,  which  causes  what  is  called 
the  *  burning '  of  the  leather. 

"  Therefore,  by  running  belts  upon  smooth  iron  pulleys,  not  only 


RULES    FOR    BELTING.  107 

the  power  to  be  transmitted  acts  destructively  upon  the  leather,  but 
other  causes  also,  which  is  not  the  case  when  leather-band  wheels  are 
employed.  The  application  of  leather  to  the  wheel  is  very  simple 
and  easy,  and  may  be  done  by  means  of  glue  by  any  intelligent  work- 
man."— Technologist,  Nov.,  1870. 

Mr.  F.  W.  Bacon  sends  us  the  following : 

80.  "A  12"  cylinder,  36"  stroke  engine,  running  66  Rpm,  with 
10-feet  fly-wheel  pulley,  drives  a  6'  6"  pulley,  19  feet  horizontally 
away,  and  8  feet  above  the  engine  shaft;  both  pulleys  of  iron, 
smoothly  turned.  Over  these  passes  a  14"  single  leather  belt,  with 
strips  2"  wide  secured  to  each  edge  of  the  outer  face ;  top  fold  of  belt 
sags  20"  from  the  straight  line  between  pulley  surfaces.  The  belt  is 
about  80  feet  long,  and  was  dressed  with  castor  oil  when  started ; 
has  been  running  4  months,  does  not  slip  under  heaviest  load,  ad- 
heres closely  to  pulleys,  even  at  the  edges,  owing  to  the  increased 
tension  put  upon  the  belt  by  the  strips.  The  engine  indicates  35  to 
40  horse-power.  At  40  it  gives  60.475  square  feet  of  belt  per  horse- 
power per  minute. 

"Another  case  which  may  be  of  interest  is  that  of  a  belt  12"  wide, 
68  feet  long,  stripped  at  the  edges  like  the  above ;  is  driven  by  a  53" 
diameter  pulley,  unturned,  around  two  pulleys  on  a  vertical  shaft, 
thence  to  a  40"  diameter  smooth-turned  pulley  at  right  angles  to  the 
driver,  which  makes  101  Rpm.  The  work  done  is  from  25  to  30 
horse-power.  The  belt  is  dressed  with  castor  oil,  and  is  ample ;  at 
30  horse-power  it  is  35.256  square  feet  of  belt  per  minute  per  horse- 
power.1' 

I  have  the  case  of  an  18-inch  diameter  by  36-inch  stroke  horizontal 
steam-engine,  running  60  Rpm,  and  indicating  77  horse-power.  It 
has  a  12-feet  pulley  fly-wheel,  over  which  runs  a  14^-inch,  much 
used,  double  leather  belt.  This  belt  drives  a  5-feet  pulley,  the  centre 
of  which  is  24^  feet  from  and  10 J  feet  above  the  centre  of  fly-wheel ; 
the  lower  fold  draws,  and  the  belt  runs  quite  freely  without  slipping. 
These  figures  give  a  velocity  of  surface  equivalent  to  35.5  square  feet 
per  horse-power  per  minute. 

A  certain  13-inch  pulley  on  a  shaft  running  203  Rpm  carries  a 
belt  2.25  inches  wide,  and  drives  a  20-inch  pulley  on  a  shaft  20  feet 
vertically  above.  The  pulleys  are  smooth  turned  iron,  and  the  belt 
of  single  leather,  with  grain  side  to  pulleys. 

This  belt  had  been  running  a  year  or  more,  under  a  tension  which 
was  limited  only  by  the  strength  of  the  lacing.  It  was  used  to  con- 


108  RULES    FOR    BELTING. 

vey  two  horse-power  to  the  upper  shaft,  but  was  considered  by  the 
lessee  to  be  unequal  to  the  task,  even  when  tightly  drawn,  and  its 
adhesion  increased  by  free  application  of  rosin. 

It  was  admitted  by  both  parties  that  the  belt  was  worked  to  its 
fullest  capacity. 

In  order  to  ascertain  the  exact  amount  of  work  done  by  the  belt, 
the  following  experiment  was  made : 

On  the  driven  shaft  above  was  a  smooth  turned  iron  pulley,  6.25 
feet  in  circumference  and  4-inch  face ;  over  this  was  thrown  a  3-inch 
leather  belt,  with  grain  side  to  pulley,  and  to  its  ends  were  attached 
unequal  weights,  such  that  the  2.25-inch  belt  was  subjected  to  its 
maximum  working-power.  These  weights  were  203  Ibs.  and  2.25  Ibs. 
Speed  of  friction  pulley  was  taken  at  132  Rpm. 

Then  we  have  132  X  6.25  =  825  ==  velocity  of  3-inch  belt  in  Fpm, 

,  825  x  200.75 

and  -  —  =  5.018  =  horse-power  of  3-mch  belt. 

33,000 

This  is  equivalent  to  a  driving-power  of  41.1  square  feet  of  belt 
per  minute  per  horse-power. 

A  single  leather  riveted  belt  of  ordinary  make  connects  a  60-inch 
to  a  30-inch  pulley  ;  both  of  smooth  turned  cast  iron :  the  centre  of 
the  latter  being  8  feet  horizontally  distant  5  feet  above  that  of  the 
former.  The  60-iiich  pulley  drives  and  makes  80  Rpm,  the  top  fold 
of  belt  sagging  13  inches  from  the  straight  line.  This  belt  does  not 
slip,  runs  with  the  hair  side  to  pulleys,  has  been  in  use  more  than  six 
years,  was  originally  9  inches  wide,  is  now  8  inches,  runs  OIIP  inch 
crooked,  and  during  the  first  two  years  of  its  existence  was  exposed 
to  the  weather,  frequently  saturated  with  water,  but  is  now  sofi  and 
adhesive  by  the  application  of  prepared  castor  oil. 

Horse-power  transmitted,  14.48  indicated,  which  is  equivalent  to 
57.826  square  feet  of  belt  travelling  per  minute  per  horse-power- 

Rule  for  Ascertaining  the  Horse-power  of  Belts,  by  Mr.  Bacon. 

We  convert  the  text  into  the  following  : 

HP  6000  _ 
v  c 

In  which  HP  =  horse-power  transmitted. 
v  =  velocity  of  belt  in  Fpm. 

c  =  contact  of  belt  with  smaller  pulley  in  lineal  feet. 
w  =  width  of  belt  in  inches. 


RULES    FOR    BELTING.  109 

Page's  Patent  Tanned  Leather  Belting. 

86.  This  excellent  belting  leather  is  made  by  Page  Brothers,  in 
Concord,  N.  H.  It  possesses  greater  pliability,  strength,  and  durabil- 
ity than  the  ordinary  tannage,  will  endure  moisture  better,  is  lighter, 
adheres  to  glue  and  cement  as  well  as  any  belting,  and,  being  softer, 
will  answer  better  for  round  belts.  It  has  been  thoroughly  and 
successfully  tried,  and  costs  no  more  than  well-made  oak-tanned 
belting. 

A  trial  showed  25  per  cent,  more  adhesive  power  than  hard  oak  or 
hemlock-tanned  leathers,  and  a  test  of  strength  proved  that,  while 
1050  Ibs.  broke  a  l|-inch  wide  oak-tanned  belt,  it  required  1850  Ibs. 
to  break  the  same  size  Page  belt. 

The  single  belts  are  ^-inch,  the  light  double  belts  ^-inch,  and  the 
heavy  double  J-inch  thick. 

The  light  double  belts,  which  are  about  the  same  price  as  best 
single,  work  well  on  cone  and  flange  pulleys,  and,  of  course,  very 
well  where  running  free  and  where  much  shifted. 

Shafts  and  Pulleys. 

"  In  the  location  of  shafts  that  are  to  be  connected  with  each  other 
by  belts,  care  should  be  taken  to  secure  a  proper  distance  one  from 
the  other.  It  is  not  easy  to  give  a  definite  rule  as  to  what  this  dis- 
tance should  be.  Some  have  this  rule :  Let  the  distance  between  the 
shafts  be  10  times  the  diameter  of  the  smaller  pulley.  But  while 
this  is  correct  for  some  cases,  there  are  many  other  cases  in  which  it 
is  not  correct.  Circumstances  generally  have  much  to  do  with  the 
arrangement,  and  the  engineer  or  machinist  must  use  his  judgment, 
making  all  things  conform,  as  far  as  may  be,  to  general  principles. 
This  distance  should  be  such  as  to  allow  of  a  gentle  sag  to  the  belt 
when  in  motion. 

"  A  general  rule  may  be  stated  thus :  Where  narrow  belts  are  to 
be  run  over  small  pulleys,  15  feet  is  a  good  average.  For  larger  belts, 
working  on  larger  pulleys,  a  distance  of  20  to  25  feet  does  well. 
Shafts  on  which  very  large  pulleys  are  to  be  placed  for  main  or  driv- 
ing belts  should  be  25  to  30  feet  apart.  We  know  of  shafting  located 
as  above  stated,  where  the  belts  work  in  a  very  satisfactory  manner, 
the  slack  side,  while  in  motion,  having  a  sag  of  1^  to  2  inches  on  the 
short  distances  above  mentioned,  while  the  larger  belts  show  a  similar 
sag  of  2^  to  4  inches,  the  main  belts  working  well  with  a  sag  of  4 
to  5  inches. 

"  If  too  great  a  distance  is  attempted,  the  weight  of  the  belt  will 


110  RULES    FOR    BELTING. 

produce  a  very  heavy  sag,  drawing  so  hard  on  the  shaft  as  to  produce 
great  friction  in  the  bearings,  while  at  the  same  time  the  belt  will 
have  an  unsteady,  flapping  motion,  which  will  destroy  both  the  belt 
and  the  machinery. 

"The  connected  shafts  should  never,  if  possible,  be  placed  one 
directly  over  the  other,  as  in  such  case  the  belt  must  be  kept  very 
tight  to  do  the  work. 

"  It  is  desirable  that  the  angle  of  the  belt  with  the  floor  should  not 
exceed  45°.  It  is  also  desirable  to  locate  the  shafting  and  machinery 
so  that  belts  shall  run  off  from  each  shaft  in  opposite  directions,  as 
this  arrangement  will  relieve  the  bearings  from  the  friction  that  would 
result  where  the  belts  all  pull  one  way  on  the  shaft. 

"  If  possible,  the  machinery  should  be  so  planned  that  the  direction 
of  the  belt  motion  shall  be  from  the  top  of  the  driving  to  the  top 
of  the  driven  pulley. 

"  All  pulleys  should  be .  carefully  centred  and  balanced  on  the 
shafting.  Driving  pulleys  on  which  are  to  be  run  shifting  belts 
should  have  a  perfectly  flat  surface.  All  other  pulleys  should  have 
a  convexity  in  the  proportion  of  about  ^  of  an  inch  to  one  foot  in 
width.  The  diameter  of  the  pulleys  should  be  as  large  as  can  be 
admitted,  provided  they  will  not  produce  a  speed  of  more  than  3000 
feet  of  belt  motion  per  minute.  When  this  speed  has  been  obtained, 
the  possible  size  of  the  pulley  may  be  reduced  in  proportion  to  the 
speed  greater  than  3000  Fpm,  as  this  speed  is  considered  the  limit 
of  economy.  The  pulley  should  be  a  little  wider  than  the  belt 
required  for  the  work.  It  is  also  well  to  consider  the  possibility  of 
adding,  at  some  future  time,  more  machinery  than  at  first  contem- 
plated, and  to  make  all  needed  provision  for  such  possible  increase. 
Such  a  course  often  proves  a  large  saving  of  expense,  or,  what  amounts 
to  the  same  thing  in  the  end,  guarantees  the  machinery  against  over- 
work. Every  pulley  not  placed  in  a  damp  room  should  be  covered 
with  a  good  leather  lagging,  put  on  by  an  experienced  workman.  A 
pulley  so  covered  is  capable  of  much  greater  and  better  results,  as  the 
belt  is  not  so  likely  to  slip.  Repeated  experiments  prove  that  the 
advantage  of  leather-covered  pulleys  over  all  others  is  fully  33 1  per 
cent. 

"  The  whole  arrangement  of  shafting  and  pulleys  should  be  under 
the  direction  of  a  mechanical  engineer,  or  a  machinist  thoroughly 
competent  for  such  work.  Destruction  of  machinery  and  belts, 
together  with  unsatisfactory  results  in  the  business,  is  a  common 
experience  which  may,  in  most  cases,  be  traced  to  want  of  knowledge 


RULES    FOR    BELTING.  Ill 

and  care  in  the  arrangements  of  the  machinery,  and  in  the  width  and 
style  of  the  belts  bought,  and  in  the  manner  of  their  use,  while  man- 
ufacturers of  the  machines  and  belts  (especially  the  latter)  are  often 
blamed  for  bad  results  which  are  caused  by  the  faulty  management 
of  the  mill  owner  himself." 

Purchasing  Belts. 

"  Having  properly  arranged  the  machinery  for  the  reception  of  the 
belts,  the  next  thing  to  be  determined  is  the  length  and  width  of  the 
belts. 

"When  it  is  not  convenient  to  measure  with  the  tape-line  the 
length  required,  the  following  rule  will  be  found  of  service :  Add  the 
diameters  of  the  two  pulleys  together,  divide  the  result  by  2,  and 
multiply  the  quotient  by  3j.  Add  the  product  to  twice  the  distance 
between  the  centres  of  the  shafts,  and  you  have  the  length  required. 

"  The  width  of  belt  needed  depends  on  three  conditions.  1st,  the 
tension  of  the  belt ;  2d,  the  size  of  the  smaller  pulley  and  the 
proportion  of  the  surface  touched  by  the  belt ;  3d,  the  speed  of 
the  belt. 

"  The  average  strain  under  which  leather  will  break  has  been 
found,  by  many  experiments  with  various  good  tannages,  to  be  3200 
Ibs.  per  square  inch  of  cross  section.  A  very  nice  quality  of  leather 
will  sustain  a  somewhat  greater  strain.  In  use  on  the  pulleys,  belts 
should  not  be  subjected  to  a  greater  strain  than  ^r  their  tensile 
strength,  or  about  290  Ibs.  to  the  square  inch  of  cross  section.  This 
will  be  55  Ibs.  average  strain  for  every  inch  in  width  of  single  belt 
T3g  inch  thick.  The  strain  allowed  for  all  widths  of  belting  —  single, 
light  double,  and  heavy  double — is  in  direct  proportion  to  the  thick- 
ness of  the  belt.  This  is  the  safe  limit ;  for  if  a  greater  strain  is 
attempted,  the  belt  is  liable  to  be  overworked,  in  which  case  the 
result  will  be  an  undue  amount  of  stretching,  tearing  out  at  the  lace 
or  hook  holes,  and  damage  to  the  joints.  When  the  belt  is  in  motion 
the  strain  on  the  working  side  will  be  greater  than  on  the  slack 
side,  and  the  average  strain  will  be  one-half  the  aggregate  of  both 
sides. 

"  The  working  adhesion  of  a  belt  to  the  pulley  will  be  in  propor- 
tion both  to  the  number  of  square  inches  of  belt  contact  with  the 
surface  of  the  pulley,  and  also  to  the  arc  of  the  circumference  of  the 
pulley  touched  by  the  belt.  This  adhesion  forms  the  basis  of  all 
right  calculation  in  ascertaining  the  width  of  belt  necessary  to  trans- 
mit a  given  horse-power.  A  single  belt  T\  inch  thick  subjected  to 


114  RULES    FOB    BELTING. 

Care  of  Belts. 

"  Belts  should  never  be  oiled  except  when  they  become  dry  and 
hard,  and  then  oil  should  be  used  very  sparingly.  Oil  not  only  rots 
the  leather,  but  it  causes  the  belt  to  stretch.  In  oiling  or  greasing  a 
belt  avoid  everything  of  a  pasty  nature.  The  belt  should  be  made 
pliable,  not  covered  with  a  sticky  substance. 

"  In  '  taking  up '  belts  observe  the  same  rules  as  in  putting  on  new 
ones. 

"  Never  add  to  the  work  of  a  belt  so  much  as  to  overload  it." 

Friction  of  Belts. 

#7.  "The  friction  of  belts  upon  pulleys  depends  upon  the  extent 
to  which  they  are  tightened,  the  extent  of  circumference  with  which 
they  are  in  contact,  and  their  breadth.  It  is  commonly  believed  that 
the  greater  the  diameter  of  pulley,  the  more  surely  does  the  belt 
cause  it  to  revolve  without  slipping.  Theoretically,  however,  and 
we  believe  practically,  it  will  be  found  that,  with  equal  degrees  of 
tightness,  equal  breadth  of  belt,  and  equal  circumstances  as  to  per- 
fection of  contact,  the  friction  of  a  belt  on  the  circumference  of  a 
pulley  is  the  same,  whatever  be  its  diameter.  The  only  circumstance 
that  can  affect  the  constancy  of  the  result,  is  that  belts  not  being 
perfectly  flexible,  lie  more  closely  to  surfaces  curved  to  a  large  radius 
than  to  those  of  smaller  radius.  When  a  certain  amount  of  power 
has  to  be  communicated  through  a  belt,  the  speed  at  which  the  belt 
moves  has  to  be  taken  into  account,  because  power  being  pressure 
multiplied  by  velocity,  the  greater  the  velocity  with  which  the  power 
is  transmitted,  the  less  the  pressure  that  has  to  be  communicated  at 
that  speed.  In  this  sense,  then,  it  appears  that  the  larger  the  pulley 
the  less  is  the  slip  of  the  belt,  because  the  greater  the  circumference 
of  the  pulley,  revolving  at  a  given  angular  velocity,  the  greater  is 
its  absolute  velocity  through  space,  and  therefore  the  less  the  pressure 
required  to  communicate  a  given  power. 

"It  is  found,  practically,  that  a  leather  belt  8  inches  wide,  embrac- 
ing half  the  circumference  of  a  smoothly  turned  iron  pulley,  and 
travelling  at  the  rate  of  100  Fpm,  can  communicate  one  horse-power. 

"  When  less  than  half  the  circumference  of  the  pulley  is  embraced, 
the  strap  must  be  proportionally  wider ;  and  when  more  than  half 
the  circumference  is  embraced,  its  width  may  be  less. 

"  The  law  according  to  which  the  friction  of  a  belt  increases  with 
an  increased  arc  of  contact,  is  of  a  peculiar  character ;  but  may  be 
readily  understood  by  comparing  the  friction  on  arcs  of  different 


RULES    FOR    BELTING.  115 

lengths.  If  a  pulley  (of  any  diameter  whatever)  were  prevented 
from  revolving,  and  a  belt  passing  over  part  of  its  circumference 
were  stretched  by  a  certain  weight  at  each  end,  additions  might  be 
made  to  the  weight  at  one  end  until  the  belt  began  to  slip  over  the 
pulley.  The  ratio  which  the  weight  so  increased  might  bear  to  the 
weight  at  the  other  end,  would  measure  the  amount  of  friction. 

"  For  example,  in  experiments  made  to  test  a  theoretical  investi- 
gation on  this  subject,  a  belt  passing  over  a  pulley  in  contact  with 
60°  of  its  circumference,  was  stretched  by  a  weight  of  10  pounds  at 
each  end.  One  of  the  weights  was  increased  until  it  amounted  to 
16  pounds,  when  the  belt  began  to  slip.  The  ratio  of  16  to  10,  or 
•J-g  =  1.6  was  then  the  measure  of  the  friction.  When  20  pounds  at 
each  end  were  used  to  stretch  the  belt,  the  one  weight  was  increased 
to  32  pounds,  giving  the  ratio  of  f  §  =  1.6,  the  same  as  before ;  and 
likewise,  when  5  pounds  were  used  for  stretching,  the  weight  at  one 
end  was  increased  to  8  pounds,  giving  still  the  same  ratio,  f  =  1.6. 
So  far,  then,  the  friction  was  precisely  proportional  to  the  stretching 
weight,  as  might  have  been  expected  from  the  ordinarily  received 
doctrine  on  the  subject  of  friction.  On  extending  the  arc  of  contact 
to  120°,  the  ratio  was  found  to  be  2.56,  or  1.63.  And  again,  on  em- 
bracing 180°  the  ratio  was  found  to  be  4.1,  or  very  nearly  1.6 3. 

"The  theoretical  investigation  brought  out  this  result  independ- 
ently, and  the  following  law  may  therefore  be  taken  as  established : 

"  If,  for  any  given  arc  of  contact,  the  one  weight  bears  to  the  other, 
at  the  point  of  slipping,  a  certain  ratio  —  for  double  the  arc,  the  ratio 
will  be  squared ;  for  triple  the  arc,  it  will  be  cubed ;  for  four  times 
the  arc  it  will  be  raised  to  the  fourth  power ;  and  so  on. 

"  In  all  cases,  however,  much  depends  on  the  tightness  of  the  belt, 
the  limits  to  the  force  with  which  it  is  strained  being,  first,  the  tensile 
strength  of  the  belt  itself,  and,  secondly,  the  amount  of  pressure  that 
it  may  be  convenient  to  throw  upon  the  shaft  and  its  bearings.  New 
belts  become  extended  by  use,  and  it  is  therefore  frequently  necessary 
to  shorten  them.  Before  use,  they  should  be  strained  for  some  time 
by  weights  suspended  from  them,  so  as  to  leave  less  room  for  exten- 
sion while  in  use.  Wherever  belts  are  employed,  they  should  be  of 
the  greatest  breadth,  and  travel  at  the  greatest  speed  consistent  with 
convenience,  as  it  is  most  important  to  have  the  requisite  strength  in 
the  form  best  suited  to  flexure,  and  the  least  possible  strain  on  the 
shafts  and  bearings. 

"  When  ropes  or  chains  are  employed,  as  in  cranes,  capstans,  wind- 
lasses, or  the  like,  for  raising  heavy  weights  or  resisting  great  strains, 


116  RULES    FOR    BELTING. 

the  requisite  amount  of  friction  is  obtained  by  coiling  them  more 
than  once  round  the  barrel  of  the  apparatus.  It  is  found  that  one 
complete  coil  of  a  rope  produces  a  friction  equivalent  to  nine  times 
the  tension  on  the  rope,  the  barrel  being  fixed.  Two  complete  coils 
of  the  rope  produces  a  friction  equivalent  to  9  x  9  times  the  tension, 
and  so  on.  The  diameter  of  the  barrel  does  not  affect  the  result. 

"Having  regard  to  these  facts,  we  may  readily  understand  the 
force  with  which  a  knot  on  a  cord  or  rope  resists  the  slip  of  the  coils 
of  which  it  consists,  for  the  several  parts  of  the  cord  act  as  small 
barrels,  round  which  the  other  parts  are  coiled ;  and  the  yielding 
nature  of  the  material  of  which  the  barrels  are  composed,  permits 
the  coils  to  become  impressed  into  their  substance  on  the  application 
of  force,  and  prevents  them  from  slipping  more  effectually  than  if 
they  were  coiled  on  a  hard  and  resisting  barrel." — From  Wylde's 
Circle  of  the  Sciences,  London. 

Mr.  A.  K.  Rider,  of  De  Lamatre  Iron  Works,  N.  Y., 
has  favored  us  with  the  following : 

88.  "  Our  rule,  which  appears  to  work  well  and  gives  very  satis- 
factory results,  is  based  on  the  assumption  that  a  belt  one  inch  wide, 
when  properly  surfaced  and  sufficiently  tight,  and  bearing  on  not  less 
than  |  the  circumference  of  smaller  pulley,  will  transmit  a  force  of 
19|  pounds  at  any  velocity.     The  power  of  a  belt,  in  foot  pounds,  is 
thus  readily  obtained  by  multiplying  its  velocity  in  Fpm  by  its  width 
in  inches,  and  again  by  19{.     The  generally  received  rule  is,  144 
square  feet  of  surface  passing  per  minute  equals  one  horse-power,  and 
the  cohesive  strength  of  good  belting  is  taken  at  4000  pounds  per 
square  inch  of  section  as  its  breaking  strength." 

From  Spon's  "  Dictionary  of  Engineering,"  p.  312. 

89.  "Belts  and  drums  form  very  effective  friction-couplings.     If 
a  machine  driven  by  a  belt  becomes  accidentally  overloaded,  the  belt 
slips  upon  the  drum,  and  a  break-down  is  generally  prevented.     By 
the  introduction  of  fast  and  loose  pulleys  the  driven  shaft  can  be  set 
in  motion  or  stopped  with  perfect  safety,  whilst  the  driving  shaft  is 
running  at  full   speed.     The  motion  of  belts  and  drums  is  much 
smoother  than  that  of  gearing,  and  they  can  be  readily  applied  to 
machines   which    require  a  high  velocity,  where   ordinary  gearing 
would  be  quite  inadmissible. 

"  The  best  description  of  leather  for  belts  is  English  ox-hide  tanned 
with  oak-bark  by  the  slow,  old-fashioned  process,  and  dressed  in  such 


RULES    FOR    BELTING.  117 

a  way  as  to  retain  firmness  and  toughness,  without  harshness  and 
rigidity.  The  prime  part  of  the  hide  only,  called  the  butt,  should  be 
used ;  these  are  cut  out  of  hides  in  the  preliminary  preparing  pro- 
cess, and  tanned  by  themselves,  afterwards  stretched  by  machinery 
and  allowed  to  dry  while  extended.  Strap-butts  of  best  leather  can 
be  permanently  elongated  4  to  5  inches. 

"  For  light  work,  belts  of  single  substance  are  sufficient,  the  strips 
of  leather  being  joined  together  by  feather-edged  splices,  first  cemented 
and  then  sewn.  Single  belting  varies  in  thickness  from  T3g  to  \  inch. 
For  heavy  work,  double  and  sometimes  treble  layers  of  leather  are 
required,  cemented  and  sewn  through  their  entire  length.  The 
material  used  for  sewing  is  either  strong,  well-waxed  hemp,  or  thin 
strips  of  hide  prepared  with  alum.  The  latter  is  generally  used  in 
the  North  of  England ;  but  its  advantages  over  good  waxed  hemp  is 
doubtful.  The  thickness  of  double  belting  is  from  -f%  to  -^  inch. 

"  An  improvement  in  the  ordinary  double  belt  has  been  introduced 
by  Messrs.  Hepburn  &  Sons,  of  Southwark,  who  have  given  much 
attention  to  this  branch  of  leather  manufacture.  It  consists  in  the 
use  of  a  corrugated  strip  of  prepared  untanned  hide  for  the  outer 
layer  of  the  belt,  and  the  usual  tanned  leather  for  the  inner  layer, 
riveted  together  by  machinery.  The  rivets  are  made  of  copper  or 
malleable  iron,  and  have  their  ends  spread,  bent,  and  driven  in  flush 
with  the  surfaces  of  the  layers.  Metallic  sewing  of  this  kind  is  also 
applied  to  double  belting  made  entirely  of  leather,  and  has  been 
found  to  work  well,  and  is  more  durable  than  ordinary  hand-sewing. 

"  The  drum  should  be  T3e-inch  per  foot  of  width,  rounding  except 
in  the  case  of  small  high-speed  pulleys,  which  should  be  |  to  |-inch. 

"  In  order  that  the  natural  tension  of  the  belts  shall  remain  con- 
stant, and  not  exceed,  though  equalling  the  value  calculated,  it  is 
requisite  to  use  tension  rollers.  The  weight,  W,  of  these  rollers  is 

*      j  i     ^  Trr      2  T  cos.  a       , 

lound  by  the  approximate  expression,  W  — — ;  wherein  a  is 

cos.  b 

half  the  obtuse  angle  A  D  B,  formed  by  the  belt  upon  which  the 
weight  rests,  and  may 
be  assumed  a  priori;  b 
the  angle  between  the 
line  A  B  and  the  hori- 
zontal line  A  C:  that 
is,  the  angle  B  A  C  = 
6,  and  T  =  tension  on 
tight  side.  Fi  14. 


118  RULES    FOB    BELTING. 

"  In  fixing  the  belt,  care  must  be  taken  to  give  it  such  a  length 
that,  when  at  repose,  it  shall  only  have  a  minimum  flexure." 

From  Leonard's  "  Mechanical  Principia"  we  make 
the  following  extracts : 

90*  "  If  the  power  to  be  transmitted  exceeds  20-horse,  and  cir- 
cumstances will  not  allow  the  centre  of  the  drums  to  be  over  15  feet 
apart,  the  power  should  be  transmitted  by  gearing." 

A  table  is  given  which  is  based  upon  the  following  data:  One 
horse-power  is  transmitted  by  belts,  1.8,  1.2,  0.9,  0.72,  0.6,  0.514, 
0.45,  0.4,  0.36  inches  wide,  if  carried  over  pulleys  2,  3,  4,  5,  6,  7,  8, 
9,  10  feet  diameter  respectively,  at  the  velocity  given  above. 

"  It  is  immaterial  whether  the  smallest  drum  is  the  driving  or  the 
driven  drum ;  if  the  diameter  of  the  smallest  drum  remains  constant, 
the  width  of  the  belt  will  remain  constant ;  if  the  diameter  of  the 
other  drum  should  be  increased  indefinitely." 

Example. 

91.  A  horizontal  "  Corliss  "  engine,  having  a  23-inch  by  48-inch 
cylinder,  making  52  Rpm,  has  an  18-feet  fly-wheel  pulley;  upon  this 
runs  a  double  leather  belt,  28  inches  wide  and  80  feet  long,  driving 
a  6-feet  diameter  pulley,  whose  centre  is  about  18  feet  horizontally 
distant,  and  whose  bottom  face  is  about  011  a  level  with  the  top  of 
the  fly-wheel  pulley  face ;  both  pulleys  of  iron,  smoothly  turned. 

The  lower  fold  of  belt  drives ;  the  top  fold  runs  quite  freely,  with 
considerable  sag. 

The  maximum  load  of  engine  is  217  indicated  horse-power,  the 
minimum  about  150.  These  figures  give  31.6  and  45.75  square  feet 
of  belt  per  minute  per  horse-power  respectively. 

Comparison  of  Single  and  Double  Belt. 

92.  A  34-inch  pulley  on  a  line  shaft  running  200  Rpm,  drives  a 
44-inch  pulley  on  a  grindstone  shaft.     The  grindstone  is  72  inches 
diameter,  its  shaft  nearly  on  same  level  as  line  shaft,  and  7  feet  4 
inches  away.     About  midway  between  these  pulleys,  a  10-inch  diam- 
eter tightener,  weighing  90  Ibs.,  rests  upon  the  top  fold  of  belt,  bear- 
ing it  down  14  inches  from  straight  line  of  pulley  faces.     This  tight- 
ener is  carried  by  a  horizontal  swinging  frame,  having  radius  arms  4 
feet  6  inches  long.     A  7-inch  single  leather  belt,  of  best  make,  was 
completely  worn  out  in  four  months,  another  lasted  seven  months, 
while  a  7-inch  double  oak-tanned  leather  belt  lasts  about  four  years. 
—  Samuel  Sevan,  at  H.  Disston  &  Sons'  Keystone  Saw-  Works,  Philada. 


RULES    FOR    BELTING.  119 

From  "Treatise  on  Mill  Gearing,"  by  Thomas  Box. 
E.  &.  F.  N.  Spon,  London,  1869. 

03.  "  The  laws  by  which  the  proportion  of  the  entire  circum- 
ference embraced  by  the  belt  governs  the  ratio  of  the  weights  T  t  are 
very  complicated.  Let 


F  =  the  co-efficient  of  friction. 

L  =  length  of  circumference  em- 
braced, in  feet  or  inches. 

jR  =  radius  of  the  pulley,  in  the 
same  terms  as  L. 

T  =  the  greater  weight  in  Fig.  15. 


Then  T=  t  x  (2.718} 


FL 
R 


(2.718) 


FL 
R 


t  =  the  lesser  weight. 

"These  formulae  cannot  be  worked  except  by  logarithms,  and  they 
then  take  the  following  forms : 

Log.  T=Loff.  t  +  ^.4343x^\\  Log.t  =  Log.  T—l  4343x^~-  \ 

"  In  the  table  on  page  120,  the  cases  of  failure  are  particularly 
instructive;  column  11  shows  that  in  all  the  cases  failure  might  have 
been  expected.  Thus,  No.  1  required  a  lOJ-inch  double  leather  belt, 
where  a  6-inch  gutta-percha  one  failed  to  do  the  work.  In  No.  2  a 
larger  pulley  was  substituted,  a  7-inch  double  leather  belt  should 
have  been  used,  and  the  6-inch  gutta-percha  one  did  the  work  badly. 
No.'  4  failed  with  a  9-inch  single  belt  to  do  the  work  for  which  a  14- 
inch  single  or  a  7-inch  double  belt  was  required.  No.  6  required  a 
10-inch  single  or  a  5-inch  double  belt,  and  failed  to  do  the  work  with 
a  6-inch  single  belt.  No.  8  required  a  13-inch  single  or  6^-inch 
double  belt,  and  failed  with  an  8-inch  single  belt.  It  will  be 
observed  that  in  cases  Nos.  1  and  11  the  difficulty  was  overcome  by 
using  larger  pulleys ;  and  in  cases  No.  4,  6,  and  8,  by  converting  the 
single  belt  into  a  double  one.  Circular  saws  and  some  other  kinds 
of  machinery  require  extra  strength  of  belt,  as  shown  by  No.  18. 

"The  rules  and  tables  we  have  given  apply  strictly  to  leather  belts 
only  ;  leather  is  in  every  way  the  best  material,  and  is  not  likely  to 
be  permanently  superseded  by  the  new  materials,  gutta-percha,  India- 
rubber,  etc. 

"  The  table  shows  that  the  power  of  a  gutta-percha  belt  -f$  or  f- 
inch  thick  is  from  25  to  50  per  cent,  greater  than  that  of  a  single 
leather  one.  We  found  in  practice  that  leather  belts  bear  about  310 
Ibs.  per  square  inch  of  section,  and  we  may  allow  that  gutta-percha 
will  bear  about  400  Ibs.  From  direct  experiments,  the  cohesive 
strength  of  gutta-percha  is  15  cwt.  or  1682  Ibs.  per  square  inch." 


120 


RULES    FOR    BELTING. 


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RULES    FOR    BELTING.  121 

Driving  Power  of  Belts. 

Let  A,  in  Fig.  15,  be  a  pulley  fixed  so  as  to  be  incapable  of  turn- 
ing, and  T  t  weights  suspended  by  a  belt  E,  which  passes  round  the 
pulley,  and  may  be  caused  to  embrace  it  more  or 
less   by   a  small   guide-pulley   D.     Let    now   the 
weight  T  be  increased  until  the  friction  of  the  belt 
is  overcome,  and  it  slips  on  the  pulley,  the  weight 
T  descending. 

The  ratio  between  T  and  t  varies  — 

1st.  With  the  co-efficient  of  friction  of  the  mate- 
rial of  the  belt  E,  sliding  on  the  material  of  the 
pulley  A.  2d.  With  the  proportion  which  the  arc 
of  the  pulley  embraced,  bears  to  the  whole  circum- 
ference of  the  pulley.  Fig.  15. 

"  It  is  independent  of  the  breadth  of  the  belt,  so 
long  as  T  and  t  remain  the  same,  but  inasmuch  as  T  and  t,  or  the 
strain  on  the  belt,  may  increase  with  the  breadth,  this  must  not  be 
understood  to  mean  that  a  narrow  belt  will  drive  as  much  as  a  wide 
one ;  for  other  things  remaining  the  same,  the  strain,  and  therefore 
the  driving  power,  varies  directly  and  simply  as  the  breadth. 

"  The  ratio  between  T  and  t  is  also  independent  of  the  diameter  of 
the  pulley,  other  things  remaining  the  same;  thus,  for  instance,  a 
strap  which  slips  on  a  pulley  1  foot  in  diameter,  with  a  weight  of  1 
cwt.  at  one  side,  and  2  cwt.  at  the  other,  would  do  the  same  on  a 
pulley  10  feet  or  any  other  diameter,  the  surfaces  being  similar. 

"  This  appears  contrary  to  our  instinctive  notions,  but  is  quite  cor- 
rect, as  I  have  proved  by  experiment.  But  this  must  not  be  under- 
stood to  .mean  that  a  small  pulley  will  carry  as  much  power  as  a 
large  one,  for  obviously,  if  both  are  set  in  motion,  making  the  same 
number  of  Kpm,  the  relative  speeds  of  belt  would  be  proportional  to 
the  diameters,  and  the  power  would  vary  in  the  same  ratio. 

"  From  Morin's  experiments  the  co-efficients  of  friction  are  as  fol- 
lows : 

.47  for  leather  belts  in  ordinary  working  order  on  wooden  pulleys 

.28  "  "  "  "  "          cast-iron       " 

.38  "  "     soft  and  moist 

.50  for  cords  or  ropes  of  hemp  on  wooden  pulleys. 

"  It  appears  from  Morin's  experiments  that  with  cast-iron  pulleys 
the  driving  power  is  the  same  whether  they  are  turned  or  not,  the 
adhesion  of  the  belt  to  the  polished  surface  generating  as  much  fric- 
tion as  with  a  rough  surface. 


122 


RULES    FOB    BELTING. 


"If  we  take  the  case  of  a  belt  in  ordinary  working  order  on  a  cast- 
iron  pulley,  the  co-efficient  of  which  is  .28,  and  calculating  for  four 
cases  in  which  the  circumference  is  successively  J,  £,  f ,  and  wholly 
embraced,  we  find  that  while  t  =  1  in  all  cases,  T  becomes  succes- 
sively 1.553  —  2.41  —  3.77  and  5.81. 

"  The  following  table  is  calculated  in  this  way,  and  gives  throughout 
the  value  of  T  when  t  =  1  for  different  kinds  of  surface  of  pulley 
and  states  of  belt.  Decimal  parts  of  circumference  of  pulley  are 
given  instead  of  fractions  named  above. 

"When  a  rope  is  used,  and  it  is  wound  more  than  once  round  the 
drum,  the  frictional  power  is  enormous ;  thus  with  a  rough  wooden 
pulley  and  a  rope  2.5  times  round  it  with  t  =  1,  T  is  2575.3. 

Table  showing  Ratio  of  Strains  on  the  Belts  of  Driving  Pulleys, 


ill 

"*•'«  fc 

NEW 
BELTS 

ON 

BELTS  IN  THE  ORDI- 
NARY STATE  ON 

SOFT 
BELTS 

ON 

ROPES  ON  WOODEN  DRUMS. 

o  of  the 
by  the  E 
circumfc 

WOODEN 
PULLEYS. 

Wooden 
Pulleys. 

Cast-iron 
Pulleys. 

CAST-IRON 
PULLEYS. 

Rough. 

Polished. 

!]| 

• 

T 

Q 

T 

Q 

T 

Q 

T 

Q 

T 

Q 

T 

Q 

.2 

1 

1.87 

.87 

1.80 

.80 

1.42 

.42 

1.61 

.61 

1.87 

.87 

1.51 

.51 

.3 

1 

2.57 

1.57 

2.43 

1.43 

1.69 

.69 

2.05 

1.05 

2.57 

1.57 

1.86 

.86 

.4 

1 

3.51 

2.51 

3.26 

2.26 

2.02 

1.02 

2.60 

1.60 

3.51 

2.51 

2.29 

1.29 

.5 

1 

4.81 

3.81 

4.38 

3.38 

2.41 

1.41 

3.30 

2.30 

4.81 

3.81 

2.82 

1.82 

.6 

1 

6.59 

5.59 

5.88 

4.88 

2.87 

1.87 

4.19 

3.19 

6.58 

5.58 

3.47 

2.47 

.7 

9.00 

8.00 

7.90 

6.90 

3.43 

2.43 

5.32 

4.32 

9.01 

8.01 

4.27 

3.27 

.8 

12.34 

11.34  !  10.62 

9.62 

4.09 

3.09 

6.75 

5.75 

12.34 

11.34 

5.25 

4.25 

.9 

16.90 

15.90 

14.27 

13.27 

4.87 

3.87 

8.57 

7.57 

16.90 

15.90 

6.46 

5.46 

1.0 

23.14 

22.14 

19.16 

18.16 

5.81 

4.81 

10.89 

9.89 

23.90 

22.90 

7.95 

6.95 

1  5 

111  31 

110  31 

2242 

21  42 

20 

1 

53547 

53447 

63  23 

62  23 

25 

1 

2575  30 

2574  30 

17852 

17752 

' 

Pulleys  in  Motion. 

"  We  have  so  far  considered  the  pulley  as  fixed ;  we  will  now  apply 
the  foregoing  facts  to  the  case  of  pulleys  in  motion.  The  mechanical 
conditions  of  a  driving  pulley,  with  half  its  circumference  embraced 
by  the  belt,  are  shown  by  Fig.  16,  in  which  we  have,  as  before,  the 
pulley  A  and  the  weight  T  and^  as  in  Fig.  15,  where  we  found  them 
to  be  respectively  1  and  2.41.  But  in  this  case,  the  pulley  A  being 
free  to  turn,  the  weights  T  and  t  being  unequal,  there  would  be  no 
equilibrium  without  an  additional  weight  at  Q,  and,  supposing  the 
drum  J  to  be  the  same  diameter  as  the  pulley  A,  it  is  self-evident 
that  the  sum  of  Q  and  t  must  be  equal  to  T ;  therefore  T  —  t  =  Q ; 
or  2.41  —  1.0  =  1.41  ==  Q. 


RULES    FOR    BELTING. 


123 


"  The  mechanical  power  transmitted  by  the  belt,  supposing  Q  to 
be  raised  by  a  rope  coiled  around  the  drum  as  a  hoist  or  windlass,  is 
the  difference  between  T  and  £,  and  Q 
might  be  increased  indefinitely,  if  we 
could  increase  T  and  t  indefinitely  in  the 
normal  proportion ;  there  is,  however,  a 
limit  to  which  this  can  be  done,  namely, 
the  cohesive  strength  of  the  strap  by 
which  the  heaviest  weight,  T,  is  carried. 
Where  leather  is  used  we  can  obtain  the 
requisite  cohesive  strength  by  increasing 
the  width  of  the  belt,  or  by  making  it  u 
double  or  treble  one,  and  this  width  must 
in  all  cases  be  proportional  to  T,  and  not 
to  t  or  to  Q. 

"  In  Fig.  16  G  may  represent  the  en-  Fig.  16. 

gine  shaft,  H  its  crank,  and  P  the  power 

which  is  equal  to  Q.  It  will  be  observed  that  the  weight  C,  or 
pressure  on  the  bearings  due  to  the  tension  on  the  two  straps,  and 
also  the  maximum  tension  T,  is  much  greater  than  the  power  P  or 
the  weight  Q. 

"If  the  weight  Q  had  been  1.0,  the  maximum  tension  T  would 

2  41 
evidently   have   been  — —  =1.71,  and   the 


minimum  tension  t  have  been 


1.0 
1.41 


=  71,  and 


thus  we  obtain  the  strain  as  shown  in  Fig.  17; 
this  is  the  most  useful  form  in  which  the 
question  can  be  put,  as  we  thus  obtain  the 
proportional  maximum  strain  or  width  of 
belt  for  a  unit  of  power  at  P. 

"  With  a  wooden  pulley  the  friction  of  the 
surfaces  is  greater,  and  the  strains  for  the 
weight  Q  are  different.  Here  for  t  =  1  we  find 
by  the  table  above  that  T  is  4.38,  and  hence 


Fig.  17. 


4.38 


=  4.38  — 1  =  3.38.     For  Q  or  P  =  l  we  should  have  T  = 


=  1.29,  and  t  = =  29 ;   so  that  with  the  same  power,  P,  a  belt 

3.38 

1.29  inch  wide,  on  a  wooden  pulley,  would  do  as  well  as  one  1.71  inch 
wide  on  a  cast-iron  one. 


124  KULES    FOR    BELTING. 

"In  the  case  of  a  pulley  of  cast-iron  with  ^  of  the  one  em- 
braced, the  table  shows  that  T  =  1.42,  and  t  being  1.0,  Q  will  be 

1  49  1 

1.42  —  1  =  .42.     For  Q  =  1  we  have  T  =  ^  =  3.38,  and  *  =  — 

===  2.38. 

"  With  a  crossed  belt  on  cast-iron  pulleys,  the  arc  embraced  being 
-j^y  of  the  circumference,  we  have  T  =  3.43,  by  table  T  —  1,  and 

343 

Q  =  2.43  ;  and  hence  with  Q  =  1,  we  obtain  T  =  -—  =  1.41,  and 

.2.4o 


"  Comparing  all  the  cases  presented  it  will  be  seen  that,  with  the 
same  engine  power,  the  breadth  of  belt  would  be  in  the  ratio  1.71, 
1.29,  3.38,  and  1.41." 

The  following  Article  from  Vol.  3,  for  1859,  "Publication  Indus- 
trielle,"  par  Armengaud  Aine",  relates  to  Belts  employed  for  the 
Transmission  of  Power: 

04.  "  Several  years  prior  to  this  date,  M.  Laborde,  M.  E.,  pre- 
sented to  the  Industrial  Society  of  Mulhouse  a  paper  on  the  subject 
of  belts,  in  which  he  made  the  following  observations  : 

"  1st.  The  resistance  to  be  overcome  must  be  less  than  the  power 
required  to  slip  the  belt  on  its  pulley. 

"  2d.   The  tension  must  not  permanently  elongate  the  belt. 

"3d.  The  tension  must  not  uselessly  increase  the  friction  of  the 
shaft  bearings. 

"  4th.  The  belt  must  be  flexible,  in  order  to  allow  of  an  easy  fold- 
ing in  all  its  parts. 

"  The  first  three  conditions  named  are  self-evident,  while  of  the 
fourth  it  may  be  said  that  a  belt  never  requires  doubling,  but  should 
always  be  composed  of  a  single  thickness  of  leather. 

"The  webs  of  a  single  leather  are  extended  and  compressed  in 
passing  over  the  pulleys  without  in  any  way  injuring  their  texture, 
while  the  two  leathers  composing  a  double  belt  are  subject  to  such  a 
friction  upon  each  other  that  their  destruction  follows  rapidly,  not- 
withstanding the  numerous  points  of  connection  uniting  both  ;  it  is 
therefore  best  to  abandon  double  belts  altogether. 

"  In  order  to  maintain  the  durability  and  flexibility  of  belts  it  is 
advised  to  apply  to  them,  as  they  need,  fine  grease,  or  ordinary  grease 
mixed  with  tallow,  which  may  be  done  while  they  are  running.  They 
are  apt  to  slip  for  a  few  minutes  after  greasing,  but  soon  adhere  again, 
and  finally  drive  the  better  for  the  application 


KULES    FOR    BELTING.  125 

"  Extended  experimental  observations  have  proved  the  superiority 
of  smooth-faced  pulleys  over  such  as  are  rough,  or  ribbed  in  the  one 
or  the  other  direction :  in  that  increased  area  of  surface  contact  with 
the  belt  is  presented  by  the  former. 

"Upon  the  above  considerations  as  a  basis,  M.  Laborde  develops 
his  formulae. 

"  1st.  The  width  of  belts  must  be  in  direct  proportion  to  the  power 
to  be  transmitted,  while  the  speed  remains  uniform. 

"  2d.   The  width  of  belts  vary  inversely  to  the  speed. 

"  Consequently  the  products  of  the  widths  and  speeds  of  belts  are 
proportional  to  the  power  transmitted  by  them. 

"  Experience  demonstrated  to  M.  Laborde  that  a  belt  3{  inches 
wide,  running  533  Fpm,  readily  transmitted  one  horse-power  of 
33,000  foot-pounds,  having  the  usual  tension,  and  without  deforming 
itself,  when  the  pulleys  are  smooth-faced  and  of  equal  diameter,  in 
order  that  the  belt  may  embrace  their  semi-circumference. 

"  This  is  equivalent  to  144.35  square  feet  of  belt  per  minute  per 
horse-power,  and  19  Ibs.  strain  per  inch  of  width. 

"  The  author  has  used  this  rule  a  number  of  years,  and  expresses 
himself  well  satisfied  with  the  result. 

"  M.  Carillon,  of  Paris,  a  mechanical  engineer  of  no  less  reputa- 
tion employs  a  rule  based  upon  the  following  statement :  A  belt  can 
transmit  one  horse-power,  if  it  have  a  surface  velocity  of  96.9  square 
feet  per  minute,  providing  not  less  than  one-third  of  the  circum- 
ference of  either  pulley  be  embraced. 

"  Notwithstanding  our  great  confidence  in  M.  Carillon's  deductions 
—  believing  that  in  most  cases  his  allowance  of  driving  surface  of 
belts  will  be  sufficient,  since  in  many  cases  belts  are  run  at  a  higher 
velocity — we  yet  think  it  preferable  to  adhere  to  the  base  established 
by  M.  Laborde. 

"  The  reduction  of  driving  surface  may  be  made  with  more  security 
by  employing  well-worked  leather,  as  that  of  Messrs.  Sterlingue  & 
Co.,  who  condense  it  under  the  hammer,  or  that  of  Mr.  Berendorf,  in 
whose  machine  it  becomes  strongly  compressed. 

"  Tables  1  and  2  (not  given  here)  are  developed  from  the  following 
example:  If  a  belt  travel  100  metres  per  minute,  it  should  be  132 
millimetres  wide  in  order  to  transmit  one  horse-power,  which  is  equiv- 
alent to  a  5.2  inch  belt  travelling  328  Fpm ;  or,  in  other  terms,  it  is 
equal  to  142.13  square  feet  of  belt  per  minute  per  horse-power. 

"  It  is  easy  to  understand  why  the  sizes  of  belts,  as  indicated  by  the 
preceding  figures,  must  be  modified  in  several  particulars.  Firstly, 


126  RULES    FOB    BELTING. 

when  the  pulleys  are  of  very  different  sizes,  or,  if  expressed  in  more 
general  terms,  when  the  pulleys  are  embraced  by  the  belt  less  than  the 
semi-circumference ;  and,* secondly,  when  the  belt  is  crossed,  or  when 
more  than  half  the  pulley  surface  is  encircled. 

"  M.  Paul  Heilmann  presented  very  judicious  observations  on  this 
subject  to  the  Society  of  Mulhouse,  which  results  are  reproduced 
in  the  Society's  Bulletin,  No.  40,  1835,  and  may  be  expressed  thus : 

"  The  friction  of  a  belt  upon  a  pulley  depends : 

"  1st.  Upon  the  pressure  or  tightening. 

"  2d.  Upon  the  number  of  degrees  of  contact. 

"  3d.  It  is  independent  of  the  diameter  of  the  pulley. 

"  4th.  It  is  independent  of  the  wMth  of  the  belt. 

"  It  is  evident  that  the  less  the  pulley  is  surrounded  by  the  belt, 
the  tighter  must  be  the  belt  in  order  to  transmit  a  given  power, 
because  the  power  which  can  be  transmitted  to  the  pulley  is  always 
less  than,  or  at  best  equal  to,  the  friction  produced  on  its  surface ; 
and  if  the  resistance  offered  by  the  machine  be  greater,  the  belt  will 
slip.  Thus  the  width  of  the  belt  has  no  other  purpose  than  to  give 
it  a  resistance  —  a  power  sufficient  to  withstand  a  certain  tension 
without  being  injured  or  broken. 

"  M.  Heilmann  says  that  this  tension,  and  with  it  the  width  of  the 
belt,  must  necessarily  be  an  inverse  proportion  to  the  numbers  as 
represented  in  the  following  table,  which  table  has  been  calculated 
after  the  formulae  and  by  the  aid  of  the  hyperbolic  logarithms. 


" Friction  =  Pe( *— \ 


"In  which,  P==  resistance  to  be  overcome. 

e  =  base  of  hyperbolic  logarithms,  =  2.718. 
/=  proportion  between  friction  and  pressure. 
R  =  radius  of  pulley. 
S—  lineal  contact  of  belt  with  pulley. 

"  This  formula  is  the  one  taught  in  the  Mechanical  Engineering 
Department  of  the  Polytechnic  College. 

"  In  the  table,  the  first  column  represents  the  angle  of  contact  of 
belt,  in  degrees  and  minutes. 

"  The  second  column  represents  the  fractional  part  of  the  circum- 
ference corresponding  to  the  angle. 

"  The  third  column  shows  the  ratio  between  friction  and  pressure 
following  the  angle  of  contact. 


RULES    FOR    BELTING. 


127 


"The  fourth  column  contains  the  result  of  the  division  of  the  ratio 
0.4670,  which  corresponds  to  the  half-circumference,  by  the  successive 
ratios  of  the  friction  and  the  pressure. 


1 

2 

3 

4 

22.30 

3^  =  0.0625 

0.0491 

9.511 

30. 

^  =  0.0833 

0.0660 

7.075 

45. 

|  =0.1250 

0.1005 

4.646 

60. 

|  =0.1667 

0.1363 

3.426 

67.30 

A  =  0.1875 

0.1545 

3.023 

90. 

$  =0.2500 

0.2112 

2.211 

112.30 

^  =  0.3125 

0.2706 

1.725 

120. 

i  =0.3333 

0.2911 

1.604 

135. 

f  =  0.3750 

0.3330 

1.402 

150. 

T5s  =  0.4166 

0.3763 

1.241 

157.30 

77e=  0.4375 

0.3983 

1.172 

180. 

4  =  0.5000 

0.4670 

1.000 

202.30 

=  0.5625 

0.5390 

0.866 

210. 

TV  =  0.5833 

0.5674 

0.823 

225. 

|  =0.6250 

0.6145 

0.760 

240. 

|  =0.6667 

0.6669 

0.700 

247.30 

i-i  —  Q.6875 

0.6937 

0.673 

270. 

|  =  o!7500 

0.7769 

0.601 

292.30 

||  =  0.8125 

0.8642 

0.510 

300. 

1  =0.8333 

0.8941 

0.522 

315. 

1  =0.8750 

0.9551 

0.489 

330. 

J.JL  =  0.9163 

1.0190 

0.458 

337.30 

j|  =  o!9375 

1.0515 

0.444 

360. 

1  =  1.0000 

1.1522 

0.405 

"  From  the  preceding  observations  it  will  be  easy  to  determine  the 
width  of  a  belt  in  all  cases  that  may  occur  in  practice  whenever  the 
maximal  force  in  horse-power  is  given,  which  is  to  be  transmitted 
and  the  speed  of  belt  known. 

"  If  the  pulleys  are  of  equal  diameters,  all  that  is  needed  is  to  find 
the  width  of  the  belt,  in  accordance  with  the  examples  from  which 
tables  1  and  2  are  constructed,  corresponding  to  speed  and  power 
required. 

"  If  the  pulleys  are  of  different  diameters,  then  use  the  following 

Rule. 

"  Determine  the  number  of  degrees  of  contact  with  the  smaller 
pulley ;  find,  in  the  third  table,  the  number  in  fourth  column  cor- 


128  RULES    FOR    BELTING. 

responding  thereto ;  multiply  the  number  thus  found  into  the  width 
of  belt  given  in  tables  1  or  2. 

"  In  all  the  preceding  we  constantly  admitted  the  belt  of  single 
thickness,  and,  consequently,  the  same  power  of  resistance. 

"  Although  this  is  generally  the  case,  yet  for  transmitting  small 
powers  at  great  speed  it  is  better  to  reduce  the  thickness  and  augment 
the  width  of  the  belts,  because  they  will  then  develop  better  on  their 
pulleys,  which  are  usually  of  small  diameters. 

"  In  such  cases  belts  of  inferior  quality  may  also  be  employed,  by 
determining  their  width  from  a  less  co-efficient  of  resistance.  On 
the  contrary,  for  the  transmission  of  great  powers  at  slow  speeds, 
it  is  advisable  to  use  the  thickest  possible  leathers,  in  order  to  avoid 
great  width. 

"  We  have,  as  yet,  taken  no  account  of  the  belt's  own  weight, 
which,  in  certain  cases,  is  to  be  added,  wholly  or  in  part,  to  the 
resistance  to  be  overcome,  whilst  in  others  it  will  have  to  be  deducted 
from  said  resistance ;  but  as  this  has  a  slight  influence  on  the  prac- 
tical results,  it  may  be  left  out  of  consideration. 

"  Belts  should  be  calculated  to  meet  the  maximal  resistance,  not 
the  average. 

Belts  of  Gut. 

"  In  speaking  of  belts,  it  will  not  be  superfluous  to  announce  that 
an  English  inventor,  Mr.  John  Edwards,  conceived  the  idea  of  making 
belts  of  gut,  prepared  in  endless  flat  bands  of  different  lengths  and 
widths,  for  use  on  pulleys,  and  united  evenly. 

"  The  filaments  of  gut  are  woven  into  ribbons  on  looms  similar 
to  those  used  in  manufacturing  metallic  gauze,  and  the  joints  made 
by  splicing,  care  being  taken  to  cut  or  burn  the  extremities  of  the 
interlaced  filaments,  in  order  to  obtain  perfectly  united  bands.  It 
is  known  that  experiments  were  made  to  manufacture  belts  from 
fibrous  substances,  such  as  hemp  and  wool,  but  it  is  thought,  up  to 
this  date,  that  they  will  not  endure  the  same  wear  and  tear  as  leather. 
The  gut  was,  and  is  yet,  employed  with  advantage  in  the  shape  of 
cords  running  in  grooved  pulleys. 

Belts  of  Wool. 

"  Another  patent  has  been  issued  in  England  to  Mr.  J.  Heywood 
for  a  system  of  belts  or  bands  of  wool,  which  the  inventor  prepares 
by  soaking  in  a  mixture  of  linseed  oil  and  rosin.  He  boils,  for 
instance,  6f  Ibs.  of  oil,  adds  4J  Ibs.  of  powdered  rosin,  and  agitates 
the  mixture  to  a  perfect  union.  After  having  the  bands  soaked,  he 


KULES    FOB    BELTING.  129 

submits  them  to  the  action  of  a  pair  of  rolls,  and  afterwards  exposes 
them  to  dry,  when  they  are  ready  for  use. 

Belts  of  Gutta-Percha. 

"  M.  M.  Rattier  &  Co.  introduce,  in  a  great  measure,  gutta-percha 
belts,  which  give  good  satisfaction.  They  also  make  these  belts  with 
wire-gauze  cores,  which  prevent  stretching.  Notwithstanding  this 
precaution,  we  believe  it  best  to  employ  such  belts  for  light  transmis- 
sion only,  with  slow  speed,  and  to  subject  them  to  slight  tensions,  in 
order  to  avoid  injury  by  heating." 

From  "  Publication  Industrielle,"  par  Armengaud  Ain6,  Vol.  9,  I860. 

05.  The  application  of  pulleys,  cones,  and  drums  for  the  trans- 
mission of  power  has  become  so  general  that,  with  cog-wheels,  they 
constitute  a  large  part  of  the  stock  of  patterns  carefully  kept  for  use. 

There  does  not  exist,  in  fact,  an  organic  means  of  transmission 
more  simple  and  inexpensive  than  that  by  the  agency  of  belts. 

In  most  cases  the  belt  and  pulley  form  a  mechanical  agent  at  once 
the  most  convenient,  the  most  easily  erected,  and  requiring  the  least 
combination  of  parts ;  it  suffices  only  that  they  be  in  exact  propor- 
tions :  1st,  to  obtain  the  necessary  speed,  and  2d,  to  communicate  the 
required  power. 

This  mode  of  transmission  has  the  advantage  of  smooth  and  quiet 
action,  of  light  weight  in  comparison  to  the  power  transmitted,  and 
of  less  liability  to  destructive  wear  and  tear,  and  consequent  accident, 
as  with  the  use  of  gearing. 

In  accordance  with  these  facts,  gearing  has  been  replaced,  of  late, 
by  belts  and  pulleys,  even  where  considerable  powers  are  transmitted. 

To  gain  all  the  advantages  which  such  a  system  is  expected  to  fur- 
nish, it  is  absolutely  necessary  to  fulfil  several  essential  conditions, 
without  which  the  best  results  cannot  be  obtained ;  for  instance,  if 
the  pulleys.be  not  of  proper  diameter,  the  speed  would  not  be  in  the 
ratio  desired ;  again,  if  the  pulley  faces  be  too  narrow  for  the  power 
transmitted,  the  belt  will  slip ;  or  if,  on  the  contrary,  all  the  dimen- 
sions be  augmented  beyond  the  requirements  of  each  case,  material 
would  be  uselessly  wasted,  and  power  continually  lost,  in  giving 
motion  to  needless  weight  of  parts. 

The  principal  questions  concerning  the  belt  and  pulley  arrange- 
ment are  the  following : 

1st.  Determine  the  diameters  of  the  pulleys  according  to  the  num- 
ber of  revolutions  their  respective  shafts  are  to  make. 
9 


130  RULES    FOR    BELTING. 

2d.  Calculate  the  dimensions  of  the  belt  according  to  the  power  it 
is  to  transmit,  and  decide  the  diameter  of  one  of  the  pulleys. 

3d.  Ascertain,  also,  the  proportions  of  the  different  principal  parts 
of  each  pulley  in  conformity  to  the  width  of  the  belt. 

The  speeds  of  pulleys  connected  by  belts  is  in  the  inverse  ratio  of 
their  diameters. 

The  width  of  belts  is  calculated  from  the  tensile  resistance  of  the 
leather.  We  merely  examine  here  the  leather  belts  most  generally 
used  in  machine  shops  and  factories. 

In  closely  observing  the  action  of  belts  on  pulleys,  it  is  found  that 
the  power  which  they  transmit  depends  on  the  amount  of  friction 
developed  on  the  surface  of  the  pulley,  and  upon  a  certain  degree  of 
tension  applied  to  the  belt  when  put  on. 

M.  Morin  has  furnished  us  with  the  following : 

1st.  If  the  belts  are  sufficiently  tightened  they  do  not  slip,  but 
transmit  the  speed  in  a  constant  ratio,  and  inversely  to  the  diameter 
of  the  pulleys. 

2d.  In  the  transmission  of  power  by  endless  rope  or  belt,  on  pul- 
leys, from  one  shaft  to  another,  the  sum  of  the  tensions  in  both  folds 
remain  constant,  in  a  manner,  that  if  the  driving  fold  is  overburden- 
ing itself,  the  driven  fold  is  relieving  itself  to  the  same  amount,  and 
that  the  sum  of  both  tensions  is  the  same  when  the  machine  is  stopped. 

3d.  The  ratio  between  friction  and  traction,  exercised  by  the  primi- 
tive tightening,  is  very  nearly  proportional  to  the  degrees  of  contact 
with  the  pulleys  when  within  the  ordinary  limits,  varying,  in  prac- 
tice, but  little  from  \  to  |  the  circumference. 

Belts  should  not  be  subjected  to  working  strains  over  284  Ibs.  per 
square  inch. 

Action  of  Belts. 

1st.  The  friction  developed  at  the  circumference  of  pulleys  is  pro- 
portional to  the  primitive  tightening  of  the  belt,  and  depends  also  on 
the  angle  in  which  the  belt  envelopes  the  pulley ;  and,  further,  on 
the  nature  and  condition  of  the  surfaces  in  contact. 

2d.  The  friction  is  independent  of  the  diameter  of  the  pulley  and 
of  the  width  of  the  belt. 

Most  of  the  belts  in  actual  use  for  transmitting  small  powers  have 
larger  dimensions  than  the  calculations  would  give,  for  the  reason 
that  belts  are  frequently  overloaded,  and  the  quality  of  the  leather 
not  always  of  the  best.  They  sometimes  are  made  to  carry  280  Ibs. 
to  the  square  inch,  instead  of  140  to  210,  to  which  latter  strains  they 
are  generally  admitted  in  practice. 


RULES    FOR    BELTING.  131 

For  the  transmission  of  great  power,  there  is  much  interest  felt  in 
employing  the  very  best  leather,  in  order  to  reduce  the  width  of  belt 
and  pulley  as  much  as  possible. 

From  "  Designing  Belt  Gearing,"  by  E.  J.  Cowling  Welch, 
we  transcribe  the  following  : 

96.     "  The  ultimate,  strength  of  ordinary  leather  belting  is  about 
3086  Ibs.  per  square  inch  ;  thus  with  belts  ^  thick  we  have  a  break- 
ing strain 

Through  the  solid  part  ..............................  675  Ibs. 

"     riveting  ................................  382   " 

"  "     lacing  ..................................  210   " 

"  Taking  a  safe  working  strain  of  say  one-third  of  each  of  these, 
we  have 

Through  the  solid  part  ..............................  225  Ibs. 

"     riveting  ................................  127   " 

"     lacing  ..................................   70   " 

"  The  working  strength  of  the  belt  must  be  taken  as  that  of  its 
weakest  part,  which  is  the  lacing." 

"  In  order  to  ascertain  the  greatest  actual  or  indicated  horse-power 
(LHP)  capable  of  being  transmitted  by  any  particular  belt,  whose 
velocity  (  F)  in  Fpm  and  breadth  (B)  in  inches  are  known,  we  ascer- 
tain the  force  (jR)  transmitted  to  the  surface  of  the  pulley  ;  then 


88,000 

"  From  the  foregoing  it  will  be  seen  that  each  unit  of  breadth  of 
the  belt  carries  its  own  tension,  and  when  this  is  at  its  maximum 
safe  amount,  and  still  we  are  not  able  to  transmit  the  required  power 
by  it,  and  we  cannot  increase  the  angle  of  contact,  or  use  a  belt  of 
sufficient  width  to  effect  the  same,  either  from  the  shaft  being  unable 
to  withstand  the  total  tension  of  the  broader  belt,  or  from  any  other 
cause  ;  we  can  only  overcome  the  difficulty  by  increasing  the  velocity 
of  the  belt  itself  —  that  is,  by  increasing  the  diameters  of  the  pulleys 
over  which  it  runs;  not  that  we  get  any  greater  adhesion  by  so  doing, 
for  increasing  the  two  pulleys  in  the  same  proportion,  the  angle  of 
contact  in  both  cases  remains  the  same,  so  also  does  the  tension;  and 
as  the  adhesion  is  independent  of  the  surfaces  of  contact,  therefore 
the  adhesion  remains  the  same,  whether  the  larger  or  smaller  pulleys 
are  used  ;  but  with  the  larger  pulleys  we  get  greater  leverage  to 


132  RULES    FOB    BELTING. 

overcome  the  resistance,  and  a  correspondingly  greater  velocity  of 
belt."—  E.  &  F.N.  Spon,  London,  1875. 

By  Z.  Allen,  Providence,  R.  I.,  from  "  Proceedings  of  N.  E. 
Cotton  Manufacturers'  Association,"  No.  10,  April  19,  1871. 

The  Relation  of  Small  Shafting  to  Hollow  Shafting. 

97.  "On  small  shafting,  pulleys  are  used  very  much  less  in 
diameter,  consequently  the  friction  of  the  shafting  is  as  its  velocity. 
If  the  circumference  of  the  pulley  is  used  for  the  bearing,  the  friction 
is  very  much  increased.  The  torsion  of  the  hollow  shafting  is  as  the 
cube  of  its  diameter ;  if  you  use  a  3-inch  shaft,  the  torsion  of  that  is 
as  its  cube.  If  you  take  from  the  centre  of  the  shaft,  you  have  left 
the  outside  shell  only,  so  that  the  amount  of  power  gained  theoreti- 
cally is  as  the  amount  of  iron  taken  from  the  inside  of  the  shaft,  run- 
ning upon  the  bearing  of  the  outer. 

"  One  difficulty  in  small  shafting  is  in  properly  fastening  the  pul- 
leys. The  construction  of  this  shafting  is  such  that  it  requires  a 
larger  diameter  to  hold  the  pulleys  than  to  transmit  the  power,  con- 
sequently I  have  taken  lT^-inch  diameter  as  the  smallest  shafting 
that  it  is  practicable  to  run  in  mills.  An  inch  shaft,  well  sustained, 
will  drive  100  looms ;  but  you  have  to  fasten  to  it  the  couplings,  the 
pulleys,  and  set-screws ;  and  if  the  holes  are  not  properly  drilled,  the 
set-screws  will  cramp  the  shaft.  After  putting  up  a  line  150  feet 
long,  it  is  necessary  to  straighten  it.  You  cannot  straighten  the  line 
of  shafting  in  the  shop,  because  the  pulleys  are  not  made  in  the  shop. 
In  order  to  straighten  the  shafting  we  take  a  lever,  put  it  under  the 
rail,  and  spring  it  into  place. 

"We  are  using  a  line  of  213g-inch  shafting,  driving  16,000  ring 
spindles.  The  quantity  of  oil  required  to  lubricate  this  shafting  is 
so  small,  that,  if  I  tell  you,  it  will  seem  almost  impossible.  I  asked 
the  overseer  how  much  oil  he  used  in  oiling  this  shafting,  and  he  told 
me  only  two  or  three  drops  to  a  bearing  once  a  week,  and  said  that 
he  would  run  the  whole  line  a  year  with  a  half-pint  of  oil. 

"I  found  one  shaft  had  been  running  eighteen  months  with  no 
dripping  pans  underneath,  the  overseer  giving  as  a  reason  that  the 
quantity  of  oil  consumed  was  so  small  that  none  were  required.  We 
all  know  that  it  requires  oil  to  run  a  shaft,  and  we  can  form  an  idea 
of  the  amount  of  friction  by  the  quantity  of  oil  consumed. 

"  The  line  of  2T3g-inch  shafting,  which  drives  16,000  spindles,  runs 
through  a  mill  350  feet  long,  and  is  fitted  up  with  bearings  8  feet 


RULES    FOR    BELTING.  133 

apart,  and  carries  a  reasonable  share  of  the  pulleys  which  drive  the 
machinery. 

"  I  have  adopted  this  method  of  having  the  main  driving  pulleys 
about  once  in  150  feet,  and  counter  lines  about  150  feet  long,  and 
belted  in  the  middle.  The  middle  shaft  is  made  2T3g-inch  diam- 
eter. 

"  If  the  pulleys  are  very  small,  it  requires,  to  run  at  a  slow  speed, 
more  power  than  it  does  through  gears,  on  account  of  the  strain 
which  you  are  obliged  to  put  upon  the  belt.  In  England  it  is  the 
custom  to  use  gears  mostly  to  transmit  the  power,  which  requires  a 
stiff  shaft  to  hold  them  in  place ;  consequently,  a  gear  never  yields ; 
it  must  go.  With  a  belt  it  is  very  different.  In  making  the  formula 
for  a  shafting,  I  adopted  as  a  standard  one-fifth  of  the  breaking  weight. 
There  is  no  pulley  put  on  strong  enough  to  run  more  than  this ;  but 
with  gears  it  must  go. 

Gearing. 

"  There  are  many  ways  of  transmitting  power  from  the  motor  to 
the  machine,  or  place  where  it  is  to  be  utilized.  I  will  invite  your 
attention  to  the  three  that  are  commonly  in  use  among  our  manufac- 
turers, viz.,  Gearing,  Shafting,  and  Belting.  Gearing  and  shafting 
transmit  a  uniform  motion,  that  is,  a  certain  number  of  revolutions, 
but  not  always  a  uniform  revolution,  owing  to  the  elasticity  of  the 
shaft  or  imperfect  construction  of  the  gearing.  Power  transmitted 
through  pulleys  by  belts  or  straps  is  variable,  and  cannot  be  relied 
upon  when  uniform  motion  is  required,  owing  to  the  elasticity  and 
thickness  of  the  belts,  and  their  liability  to  slip.  Power  transmitted 
through  gears  and  pulleys  may  have  an  increased  or  diminished 
velocity  by  having  gears  and  pulleys  of  different  diameters.  But 
with  shafting  the  velocity  is  positive,  as  by  construction  both  ends  of 
the  shaft  must  run  with  the  same  number  of  revolutions.  Each  of 
these  methods  has  its  advantages,  but  neither  motion  in  all  cases  can 
be  made  to  supply  the  place  of  the  others.  When  a  positive  ratio  is 
required,  between  the  driver  and  driven,  it  must  be  through  gears ; 
and  as  gears  are  universally  used  to  transmit  power  from  the  water- 
wheel  or  water-wheel  shaft  to  the  second  mover,  let  us  for  a  few  minutes 
consider  gears  and  their  formation.  Possibly  no  part  of  mechanical 
science  in  common  use  is  so  poorly  understood  or  wretchedly  abused  as 
the  formation  of  gearing.  Each  draftsman  or  mechanic  has  his  favorite 
tooth  or  form  of  tooth.  It  is  his  pet  child,  and  there  is  no  other  like 
it.  To  ask  him  to  demonstrate  or  explain  why  it  is  better,  would  be 
considered  almost  an  insult ;  but  however  perfect  it  may  be  in  theory 


134  RULES    FOR    BELTING. 

and  construction,  if  the  gears  are  not  properly  adjusted  to  each  other, 
and  made  to  run  as  designed,  the  whole  theory  and  mechanism 
becomes  useless,  as  the  teeth  are  formed  for  a  definite  pitch  and  can- 
not be  used  for  any  other,  either  theoretically  or  practically,  when  a. 
smooth  motion  is  required. 

"  In  forming  teeth  for  gears  we  first  draw  what  is  called  the  pitch 
line,  or  circumference  of  uniform  motion,  which  is  the  working  diam- 
eter of  the  gears.  The  teeth  are  formed  from  this  line,  and  it  is 
indispensable  to  the  smooth  running  of  the  gears  that  these  lines 
should  run  together,  otherwise  there  would  be  a  grumbling  noise  or 
jar,  like  the  rolling  of  a  fluted  roll  over  a  plain  hard  surface.  I 
think  I  can  demonstrate  to  any  geometrician,  that  a  tooth  similar  to 
the  epicycloidal  and  hypocycloidal  tooth  is  the  only  one  that  can  be 
made  to  run  smoothly. 

"This  tooth  is  formed  by  having  two  circumferences  run  together, 
corresponding  to  the  pitch  line  or  diameter  of  the  required  gears. 
However,  as  this  is  not  the  proper  place  to  discuss  theories,  I  will  not 
occupy  your  time  by  doing  so.  Within  the  last  month  I  have  started 
a  new  Turbine  water-wheel  of  about  350  horse-power.  The  crown, 
gear  7  feet  diameter,  and  jack  gear  4  feet  diameter.  The  teeth  in 
these  gears  are  parallel  below  the  pitch  line,  and  when  started  they 
did  not  run  smoothly.  I  had  them  ground  together  with  tallow  and 
emery,  and  they  at  once  commenced  forming  a  tooth  similar  to  the 
epicycloidal  tooth. 

"  In  discussing  the  properties  of  gears,  I  have  come  to  the  following 
conclusions :  First,  That  the  loss  by  transmitting  power  through  gears 
is  1^  per  cent,  in  the  driver,  1^  per  cent,  in  the  driven,  and  1 J  per  cent, 
in  the  teeth,  in  all  4^  per  cent. ;  i.  e.,  when  the  diameter  at  the  pitch 
line  is  eight  (8)  times  that  of  the  bearing.  If  the  diameter  is  only 
four  to  one,  then  the  loss  is  double,  or  9  per  cent.;  i.  e.,  the  friction 
or  loss  of  power  is  inversely,  as  the  ratio  of  the  diameter  of  gears  to 
their  bearings.  In  this  statement  I  have  not  considered  the  weight 
of  the  gears  or  shaft.  In  horizontal  shafting  the  weight  has  no  effect, 
as  the  weight  of  the  gear  seldom  is  equal  to  the  pressure  upon  the 
teeth. 

•'  Secondly.  If  intermediate  gears  are  used  in  transmitting  power, 
and  the  three  axes  are  in  the  same  plane,  the  friction  is  double,  or  9 
per  cent,  in  lieu  of  4|  per  cent.  If  the  driver  and  driven  have  differ- 
ent diameters,  the  opposite  sides  of  the  teeth  in  the  intermediate  must 
be  of  a  different  shape,  i.  e.,  made  to  conform  to  the  different  diam- 
eters of  the  driver  and  driven. 


RULES    FOB    BELTING.  135 

"Thirdly,  for  the  same  reason,  the  driver  cannot  admit  of  two 
driven  gears  of  different  diameters  at  the  same  time  and  run 
smoothly. 

"As  the  destroying  force  or  concussion  is  as  the  square  of  the 
velocity,  and  velocity  of  contact  is  to  the  pitch  of  teeth,  as  verse  sine 
to  sine.  I  have  therefore  adopted,  to  transmit  the  greatest  amount 
of  power  with  regard  to  durability,  the  following  formula  for  first 
drivers,  and  made  tables  to  correspond.  Let  d  =  diameter  in  feet, 
p  —  pitch  in  feet,  and  HP  =  horse-power  :  then 


and  to  find  the  velocity  of  the  periphery  in  feet,  multiply  the  square 
root  of  the  diameter  by  750  feet,  or  750  ^~T=  V)  and 


6 

i.  e.,  if  the  pitch  and  velocity  are  obtained  by  the  above  rule,  and 
the  breadth  is  2J  times  the  pitch,  which  I  think  will  be  found  correct 
for  spurs,  and  2|  for  bevel  gears. 

"  Usually,  I  think  the  pitch  of  gears  is  too  large  for  the  diameter 
to  insure  good  results.  An  increased  pitch  on  the  same  diameter  will 
not  transmit  more  power,  as  the  velocity  will  have  to  be  diminished 
to  make  it  run  smoothly.  These  formulas  are  intended  for  the  smaller 
gear,  the  larger  is  not  to  be  considered. 

"  There  are  advocates  for  the  rolling  of  gears  together,  i.  e.,  the 
teeth  can  be  so  formed  that  one  tooth  can  be  made  to  roll  into  the 
other ;  but  I  think  this  can  be  shown  to  be  theoretically  and  practi- 
cally impossible. 

"  If  spur  gears  are  firmly  sustained  and  well  adjusted,  and  the 
teeth  actually  cut  in  the  epicycloidal  form,  33  per  cent,  can  be  added 
to  the  velocity  indicated  in  the  following  table.  This  will  increase 
the  horse-power  in  the  same  ratio. 


136 


RULES    FOR    BELTING. 


Table  showing  the  Diameter,  No.  of  Teeth,  Pitch,  Velocity,  Revolutions  and 
Horse-Power  of  Gears. 

Let  D  =  diameter  in  feet.     T=No.  teeth.     P—  pitch  in  inches. 
V  =  velocity  of  periphery  in  feet ;  and  HP  =  horse-power. 


Diameter 
in  Feet. 

No.  of 
Teeth. 

Pitch  in  Inches. 

Velocity  of 
Periphery  in 
feet  per  minute. 

Revolutions 
per  minute. 

Horse-power. 

1 

22 

1.72+ 

750 

238.8 

44 

14 

26 

2.15+ 

915 

194.7 

86 

2 

30 

2.53+ 

1057 

168.3 

137 

21 

33 

2.86+ 

1187 

151.1 

197 

3 

36 

3.16+ 

1299 

137.8 

263 

H 

38 

3.43+ 

1403 

127.5 

337 

4 

41 

3.69+ 

1500 

119.3 

414 

44 

43 

3.93+ 

1591 

112.5 

499 

5 

45 

4.16+ 

1677 

106.7 

590 

5£ 

47 

4.38+ 

1759 

101.7 

682 

6 

49 

4.59+ 

1837 

97.4 

783 

*4 

51 

4.74+ 

1912 

92.6 

993 

7 

53 

4.98+ 

1984 

90.2 

1004 

71 

65 

5.16+ 

2053 

87.1 

1115 

8 

56 

5.34+ 

2121 

84.4 

1233 

*4 

58 

5.52+ 

2186 

81.8 

1357 

9 

59 

5.68+ 

2250 

79.5 

1483 

9£ 

61 

5.85+ 

2311 

77.4 

1607 

10 

62 

6.01  + 

2371 

75.4 

1738 

10J 

64 

6.16+ 

2430 

73.6 

1876 

11 

66 

6.31  + 

2488 

71.9 

2020 

114 

67 

6.46+ 

2543 

70.3 

2167 

12 

68 

6.61  + 

2598 

68.9 

2311 

124 

70 

6.75+ 

2651 

67.5 

2462 

13 

71 

6.89+ 

2704 

66.2 

2610 

184 

72 

7.02+ 

2755 

64.9 

2773 

14 

74 

7.16+ 

2806 

63.8 

2932 

144 

75 

7.30+ 

2856 

62.7 

3099 

15 

76 

7.44+ 

2904 

61.6 

3262 

JS4 

77 

7.55+ 

2953 

60.6 

3429 

16 

79 

7.68+ 

3000 

59.6 

3604 

Shafting. 

"  We  will  next  consider  shafting  and  the  transmission  of  power 
through  the  same,  the  theory  of  which,  I  presume,  is  well  understood 
by  you  all ;  it  is,  therefore,  only  in  the  adaptation  that  I  may  differ 
with  some  or  all  of  you. 

"  Wrought-iron  shafting  of  one  inch  diameter  will  transmit  from 


RULES    FOR    BELTING.  137 

14  to  15  horse-power  at  100  Rpm  before  there  is  any  set  twist.  You 
will  observe  by  this  that  a  shaft  is  seldom  twisted  off,  but  is  usually 
broken  by  jar  of  gears,  or  being  out  of  line,  or  by  transverse  pressure. 
A  shaft  2  inches  diameter,  100  revolutions,  will  transmit  100  horse- 
power before  there  is  any  set  twist.  A  shaft  4  inches  diameter, 
100  revolutions,  will  transmit  800  horse-power  before  twisting,  but 
will  frequently  be  broken  with  very  much  less  power  if  out  of 
line  ;  while  1  inch  to  2  inch  shafting,  being  flexible,  will  hardly 
be  influenced  by  small  variations.  You  will  perceive  from  this 
that  torsion  is  hardly  to  be  considered  in  shafting  a  mill,  as  it 
will  require  larger  shafting  to  prevent  springing  by  transverse  pres- 
sure than  it  does  for  torsion.  With  prime  movers,  or  wheel  shafts, 
we  can  afford  to  pay  an  extra  insurance  in  loss  of  power  and 
weight  of  iron,  as  there  is  usually  but  one  or  two  in  the  mill,  and 
should  any  accident  occur  to  these  it  would  cause  the  stopping  of  the 
mill,  and  the  loss  might  cost  the  price  of  a  dozen  shafts.  I  have, 
therefore,  taken  one-fifteenth  (-fa)  of  the  twisting  weight,  or  the  cube 


J3   y     ~L> 

of  the  diameter,  etc.,  -  =  HP. 

100  d3  x  2  x  B 

For  second  movers  we  have  the  formula  --  —  —  --  =  HP. 

d3  x  8  x  R 

For  third  movers,  or  mill  shafting,  -  =  HP. 

100 

"  In  advocating  small  shafting  I  do  not  pretend  that,  theoretically, 
there  is  any  saving  of  friction  in  transmitting  the  same  amount  of 
power.  It  requires  the  same  amount  of  friction  for  a  1-inch  shaft  as 
it  does  for  a  6-inch  shaft,  if  both  are  equally  strained,  as  a  6-inch 
shaft,  of  course,  would  run  very  much  slower  to  transmit  the  same 
amount  of  power,  but  that  in  most  cases  the  diameter  is  larger  than 
is  required,  as  the  transverse  pressure  requires  a  larger  diameter  than 
the  torsional,  as  before  stated. 

"  This  led  me  to  consider  if  there  might  not  be  some  way  devised 
to  meet  this  difficulty.  In  most  of  our  mills  the  bays  are  about  8  feet, 
and  require  shafting  of  about  2  inches  diameter  to  sustain  the  lateral 
pressure  of  a  card  or  loom  belt  ;  yet  this  same  shaft  has  torsional 
strength,  at  150  revolutions,  to  run  900  looms  before  twisting,  although 
it  may  not  be  running  more  than  8  to  10  looms  or  cards  when  near 
the  end  of  the  line,  while  a  shaft  |  inch  diameter  is  all  that  is  re- 
quired to  perform  that  amount  of  work,  if  well  sustained.  To  meet 
the  difficulty  I  have  made  a  cast-iron  rail,  so  constructed  that  the 
hangers  slide  along  the  whole  length  of  the  line  without  regard  to 
the  beams.  By  this  arrangement  there  can  be  as  many  hangers  as 


138  RULES    FOR    BELTING. 

are  required  —  one  to  each  pulley,  if  necessary.  The  number  of 
bearings  do  not  increase  the  friction  if  properly  arranged,  as  it  is  by 
this  rail.  I  use  this  rail  for  all  shafting  less  than  1 J  inches  diameter, 
where  the  bays  are  8  feet.  I  have  running  2  lines,  160  feet  each, 
each  line  driving  60  breaker  cards  and  lap  bead.  Its  diameter  is 
lT3g  inches  to  1^- inches,  and  runs  280  Rpm  ;  driving  pulleys  on  shaft- 
ing for  cards,  7  inches  diameter.  I  have  also  about  1500  feet  more 
driving  cards  and  looms;  about  half  of  it  has  run  16  months  without 
any  repairs.  I  would  here  state  shafting  might  be  much  smaller  but 
for  the  difficulty  of  having  it  made  thoroughly  in  our  workshops. 
The  pulleys  must  be  well  balanced  and  nicely  bored,  or  the  set-screws 
or  keys  will  spring  the  shaft. 

"  I  use  this  rail  in  connection  with  shafting  for  cards  and  looms.  It 
is  not  so  necessary  for  spinning  and  other  machinery,  as  the  machines 
or  pulleys  on  them  are  a  greater  distance  from  each  other.  I  have, 
in  one  of  the  Lawrence  Manufacturing  Co.'s  mills,  a  shaft  2T3g  inches 
diameter,  running  416  Rpm,  in  common  Babbitt  boxes,  driving  14,000 
ring  spindles,  If-inch  ring.  This  shaft  has  run  18  months  without 
any  repairs  or  extra  labor  whatever.  It  has  no  self-oilers,  but  is 
oiled  once  a  week  with  a  common  oil-can,  using  a  mixed  oil  of  2 
parts  sperm  and  1  part  Downer's  paraffine. 

"  We  have  another  line  of  shafting  300  feet  long,  2|-  inches  diam- 
eter, running  433  Rpm,  driving  15,000  throstle  and  mule  spindles, 
with  full  complement  of  machinery.  This  shaft  has  run  about  10 
months ;  about  ^  of  it  was  not  under  cover,  being  exposed  to  the 
cold  weather  of  last  winter.  This  line  has  given  no  trouble.  I  have 
yet  to  see  a  shaft  less  than  2|  inches  diameter  twisted  off,  and  hope 
if  any  one  present  has  they  will  state  the  fact  and  circumstances  to 
the  meeting.  I  have  often  seen  larger  ones  broken  by  being  out  of 
line,  and  I  think  this  is  one  of  the  strongest  arguments  in  favor  of 
small  shafting.  I  think  J  of  the  friction  and  |  of  the  weight  of  the 
shaft  can  be  saved  over  the  old  system  of  small  and  quick  shafting 
well  arranged.  One  can  hardly  afford  to  waste  a  large  amount  of 
power  to  drive  the  heavy  shafting  of  a  large  mill  to  prevent  an  outlay 
once  a  year  or  so  of  some  small  accident  that  may  possibly  occur. 
And,  furthermore,  I  claim  it  is  better  that  a  small  shaft  should 
break  than  hold  so  firmly,  as  in  case  of  a  large  shaft  it  would  do,  as 
to  cause  injury  either  to  life  or  machinery,  as  the  case  may  be.  Self- 
protection  is  the  first  law  of  nature,  we  are  told,  hence  civil  engineers 
always  construct  mills  with  a  view  that  nothing  shall  give  out  in  the 
future  —  no  matter  what  its  present  cost  in  material  and  power  —  as 


RULES    FOR    BELTING. 


139 


they  know  full  well  their  reputation  is  at  stake ;  and  should  any  of 
their  work  need  renewing  in  a  year  or  so,  they  would  be  condemned. 
Furthermore,  they  construct  with  the  knowledge  that  inferior  capaci- 
ties may  run  the  machinery,  and  we  all  know  by  experience  what  and 
how  great  those  difficulties  are. 

Horse-Power  of  Shafts — Speed  100  Revolutions  per  Minute. 


FIRST  MOVERS. 

SECOND   MOVERS. 

THIRD  MOVERS. 

DIAM. 

HORSE- 
POWER. 

DIAM. 

HORSE- 
POWER. 

DIAM. 

HORSE- 
POWER. 

DIAM. 

HORSE- 
POWER. 

Inches. 

Inches. 

Inches. 

Inches. 

3 

27.00 

31.25 

1 

3.00 

2j| 

66.35 

31 

34.33 

2! 

41.59 

l_Jg 

3.59 

2| 

71.29 

3£ 

42.87 

3 

54.00 

IJ 

4.27 

m 

76.04 

3| 

52.73 

31 

68.66 

^A 

5.02 

3 

81.00 

4 

64.00 

3| 

85.74 

lj 

5.85 

STS" 

86.16 

41 

76.76 

3| 

105.46 

IT^. 

6.78 

3i 

91.38 

41 

91.12 

4 

128.00 

if 

7.79 

3A 

97.15 

4? 

107.17 

4? 

153.52 

8.91 

102.98 

5 

125.00 

4^ 

182.24 

i* 

10.12 

3A 

109.04 

51 

144.70 

43 

214.34 

1_9 

11.19 

3| 

115.33 

5^ 

166.37 

54 

250.00 

1| 

12.87 

3T7_ 

121.10 

5| 

190.10 

51 

289.40 

1-j-J. 

14.41 

3J 

128.62 

6 

216.00 

5J 

332.74 

If 

16.07 

3_9 

135.63 

61 

244.14 

5| 

380.20 

1I| 

17.86 

3fl 

142.90 

6! 

274.62 

6 

432.00 

IJ 

19.77 

150.42 

307.54 

(>i 

488.28 

HI 

21.81 

8I! 

158.20 

74 

343.00 

6^ 

549.24 

2 

24.00 

166.24 

7| 

381.07 

6| 

615.08 

2TJg 

26.32 

3g 

174.55 

7^ 

421.87 

7 

686.00 

2-i 

28.78 

4§ 

183.13 

7| 

465.48 

71 

762.14 

2T3g 

31.40 

4 

192.00 

8 

512.00 

7| 

843.74 

O  ] 

34.17 

4Tig 

201.12 

8| 

561.51 

930.96 

2T5g 

37.09 

4g 

210.56 

8| 

614.12 
669.92 

84 

1024.00 
1123.02 

O  3 

40.18 
43.44 

I 

220.28 
230.29 

9 

729.00 

8^ 

1228.24 

o  j 

46.87 

240.60 

9| 

791.45 

8| 

1339.84 

2^ 

50.47 

H 

251.22 

857.37 

9 

1458.00 

2| 

54.26 

262.14 

9| 

926.86 

2^-J- 

58.23 

4B 

273.37 

10 

1000.00 

2| 

62.39 

The  Transmission  of  Power  from  Motors  to  Machines. 

"  It  will  be  instructive  to  you,  as  superintendents  of  the  present 
improved  machinery  of  mills,  to  look  back  on  the  imperfect  modes 
of  transmitting  power  early  used  in  the  commencement  of  the  cotton 
manufacture  in  New  England. 


140  RULES    FOR    BELTING. 

"  So  cheap  and  abundant  was  water-power  then  that  steam-power 
was  not  at  first  resorted  to. 

"  It  was  deemed  necessary  to  locate  a  mill  directly  over  the  water- 
wheels,  so  that  a  main  upright  shaft  might  be  arranged  upward 
through  the  several  stories,  to  transmit  the  power  more  directly  to  a 
main  horizontal  shaft  in  each  room,  to  distribute  power  to  each 
machine. 

"The  shaftings  were  all  made  square,  to  receive  the  cast-iron 
wheels  fastened  by  wedges.  The  pulleys  were  made  of  wood,  by 
clamping  together  pieces  of  joists,  notched  to  fit  the  shafts,  by  means 
of  screw-bolts.  Instead  of  the  numerous  light  pulleys  now  used, 
long  wooden  drums  were  built  around  the  shafts,  and  made  of  boards 
nailed  upon  circular  plank  heads.  With  the  slow  speed  of  40  or  50 
turns  per  minute,  some  of  these  drums  were  necessarily  made  3  or 
4  feet  diameter  and  several  feet  long,  darkening  the  rooms  by  their 
ponderous  magnitudes,  and  requiring  very  high  ceilings  to  admit 
them. 

"  These  great  drums  being  frailly  nailed  together  and  unbalanced, 
could  not  be  used  with  quick-revolving  movements  without  shaking 
them  to  pieces,  and  also  shaking  the  floors  intolerably. 

"  This  was  the  style  of  mill  shafting  and  pulleys  in  use  when  I  first 
commenced  building  a  mill  at  Allendale,  in  the  year  1822. 

"  Cast-iron  pulleys,  clamped  upon  the  shafting,  were  soon  after 
introduced,  with  their  faces  smoothed  by  grinding  on  stones.  Round 
iron  shafts  were  deemed  a  great  improvement,  with  drilled  wheels 
and  pulleys  fitted  to  them.  With  these  advantages,  the  speed  of  the 
horizontal  shafts  was  augmented  to  produce  80  or  90  Rpm.  Early 
experiences  of  the  troublesome  difficulties  in  operating  a  manufactory, 
resulting  from  the  imperfect  modes  of  mill  gearing  then  in  use, 
excited  an  impatience  of  longer  enduring. 

The  Disadvantages  of  Transmission  of  Power  from  Motors  to  Machines 
with  Slow  Speed. 

"In  all  calculations  of  the  strength  of  shaftings,  wheels,  and 
pulleys  there  is  a  certain  relationship  between  the  velocity  of  their 
movements  and  transmission  of  power.  A  belt,  shaft,  or  a  pulley 
that  makes  one  revolution  to  do  the  same  work  which  is  done  by 
another  making  2  revolutions,  has  double  the  stress  imposed  upon  it, 
and  must  have  double  the  strength.  By  doubling  the  speed  there  is 
an  opportunity  of  economizing  the  weight  and  costs  of  the  materials 
employed  for  mill  gearing  in  a  somewhat  corresponding  ratio.  These 


RULES    FOR    BELTING.  141 

are  strong  incentives  to  incite  us  to  attempt  improvements  of  trans- 
mission of  power  in  all  manufactories. 

"In  the  functions  of  the  mechanisms  of  all  animals  the  most 
admirable  scientific  skill  is  displayed  in  adapting  the  proportion  of 
bone  and  muscle  to  the  speed  of  movement  designed  to  be  accom- 
plished. These  are  models  for  study  presented  to  the  engineer  for 
copying,  in  artificial  mechanisms  for  transmitting  power.  The  slender 
limbs  of  the  deer,  of  the  greyhound,  and  race-horse  —  all  designed  for 
fleet  movements  —  show  an  impressive  contrast  with  those  of  the  ele- 
phant or  the  heavy  draught-horse. 

"  Instead  of  increasing  strength  of  wheels  and  pulleys  by  additions 
of  more  metal,  when  they  are  to  be  used  with  a  higher  speed,  they 
become  less  fit  for  turning  with  swift  velocities.  They  may  even  fly 
into  pieces  by  the  tendency  of  this  excess  of  matter  to  move  in  a 
straight  line,  recognized  as  '  centrifugal  force.' 

"  To  duly  apportion  the  formation  of  the  parts  of  all  machines  for 
the  transmission  of  power,  is  the  scientific  task  assigned  to  engineers. 
In  addition,  there  is  requisite  a  knowledge  of  the  various  properties 
of  strength,  elasticity,  and  hardness  to  endure  wear,  and  other  quali- 
ties. Even  changes  of  temperature,  with  consequent  expansion  and 
contraction  of  metallic  parts,  is  not  to  be  overlooked.  The  imper- 
fections of  settling  foundations,  by  disarranging  the  best  fitted  lines 
of  strong  shafting,  may  cause  them  to  fail  of  durably  transmitting 
power  from  motors  to  machines.  The  very  rigidity  of  the  parts, 
resulting  from  the  great  size  of  shaftings  requisite  for  transmitting 
power  with  slow  velocities,  is  a  principal  cause  of  their  failure,  where 
light  and  flexible  shafting,  with  high  velocities,  might  durably  per- 
form the  service.  I  will  here  give  you  a  remarkable  illustration  of 
the  actual  results  of  transmitting  power  by  mill  gearing,  with  slow 
speed,  by  the  strongest  shafting,  made  without  regard  to  cost  for 
securing  durability  of  service. 

"In  persistently  carrying  out  the  old  system  of  heavy  shafting 
with  slow  velocities,  in  a  large  cotton-mill  built  in  Connecticut,  in 
the  year  1857,  the  attempt  was  made  to  transmit  the  power  from 
four  large  water-wheels  through  a  line  of  cast-iron  shafting  of  the 
great  diameter  of  12  inches,  made  in  sections  of  10  feet  in  length, 
each  piece  weighing  3500  Ibs.,  with  couplings  of  the  weight  of  3800 
Ibs.  each.  So  great  was  their  weight  and  rigidity,  that  the  settlings 
of  the  foundations,  changes  of  temperature,  and  continual  jar  caused 
them  to  break  so  frequently  as  to  render  necessary  the  replacement 
of  them  by  new  wrought-iron  shafts.  Quite  recently  these,  in  turn, 

OK   THK 


-4UFO 


142 


RULES    FOR    BELTING. 


have  been  discarded  as  unsatisfactory,  and  are  superseded  by  light, 
quickly-revolving  shaftings,  driven  by  belts  from  pulleys  20  feet 
diameter  and  24-inch  face,  with  a  surface  velocity  of  over  5000 
Fpm.  All  that  was  practicable  to  perfect  the  old  system  of  slow 
speed  of  mill  gearing  was  here  done  to  maintain  a  dying  struggle  for 
its  prolonged  existence. 

Experiments  for  Testing  the  Advantages  of  Transmitting  Power  with  High 

Velocities. 

"  Having  realized,  from  practical  experiences,  the  disadvantages 
of  the  slow  speed  system,  more  than  twenty  years  previously  to  this 
persistent  attempt  to  perpetuate  it,  an  entirely  opposite  system  was 
commenced  by  me  in  the  construction  of  a  second  mill  at  Allendale, 
in  the  year  1839.  The  idea  was  there  carried  out  of  more  than 
doubling  the  then  existing  speed  of  mill  shafting,  from  90  revolu- 
tions to  over  200  per  minute,  for  the  special  purpose  of  reducing  the 
size  and  weight  of  all  the  shafting  and  pulleys  in  nearly  a  corre- 
sponding ratio,  with  the  economy  of  costs  and  motive  power. 

"To  accomplish  this  object,  several  important  innovations  were 
necessary  upon  the  old  modes  of  transmitting  power.  A  wheel-pit 
was  requisite  outside  of  the  mill  building,  in  a  separate  wheel-house, 
for  the  double  purpose  of  obtaining  more  space  for  larger  cog- 
wheels, to  get  up  the  requisite  speed,  and  of  excluding  the  noxious 
steamy  dampness  arising  from  all  water-wheels  shut  up  within  the 
mill  walls. 

"  The  pulleys  in  previous  use,  with  ground  or  turned  surfaces, 
would  not  operate  quietly,  without  being  turned  inside  as  well  as  out- 
side, to  balance  the  rims,  and  prevent  the  tremor  consequent  on  the 
use  of  all  unbalanced  pulleys  revolving  rapidly.  This  improvement 
also  reduced  the  weight  of  the  pulleys  to  correspond  with  the  reduced 
weight  of  the  shafting  and  wheels,  made  of  half  the  previous  diam- 
eters, excepting  those  used  in  the  wheel-pits  of  larger  size  to  get  up 
speed. 

"  Before  this  systematic  balancing  of  pulleys  was  commenced,  no 
inconsiderable  portion  of  the  power  was  transmitted  to  shake  the 
floors,  and  even  to  cause  some  of  the  old  wooden  mills  to  rock  to  and 
fro.  This  experiment,  deemed  somewhat  wild  at  the  time,  proved 
successful.  It  has  gradually  been  adopted  as  an  economical  system 
of  transmitting  power  from  motors  to  machines  by  high  velocities 
of  shafts  and  belts. 

"  In  constructing  a  third  mill  in  Georgiaville,  in  the  year  1853,  a 


RULES    FOR    BELTING.  143 

further  attempt  was  made  to  more  than  double  the  speed  again,  and 
to  still  further  economize  the  weights  and  cost  of  materials  and  power 
used. 

"  The  details  of  the  experiments  there  made  and  practically 
applied,  you  have  requested  me  to  give  an  account  of,  as  facts  that 
may  serve  usefully  for  guidance  hereafter  to  others,  in  further  per- 
fecting the  transmission  of  power  for  operating  the  machinery  of 
mills. 

System  Pursued  in  Transmitting  Power  from  Motors  to  the  Manufactory. 

"  In  the  location  of  mills  on  water-courses,  it  has  commonly  been 
deemed  necessary  to  place  the  main  building  directly  over  the  spots 
where  the  wheel-pits  are  unavoidably  located,  on  some  steep  hill-side, 
or  rocky  precipice,  however  unfavorable  the  site  may  be  for  grading 
and  for  costly  foundations,  with  dark  and  damp  basement-rooms, 
unsuitable  for  occupancy  by  workmen. 

"  One  of  the  most  important  advantages  derivable  from  the  new 
system  of  transmitting  power  economically  to  a  distance  from  water- 
wheels  as  motors,  is  practically  available  in  selecting  a  good  level  site 
for  the  location  of  a  manufactory. 

"  In  carrying  out  this  system  at  Georgiaville,  the  power  has  been 
transmitted  several  hundred  feet  from  a  bluff,  where  a  fall  of  water 
of  36  feet  descent  was  available  by  two  successive  falls  of  20  and  16 
feet  each.  To  accomplish  this  task,  with  the  massive  shafts  and 
couplings  then  in  common  use  (1852),  appeared  to  be  too  costly  and 
difficult  of  execution  with  satisfactory  results. 

"  Encouraged  by  previous  experiments  for  practically  transmitting 
power  by  swiftly-revolving  shafts  and  belts,  the  attempt  was  boldly 
made  to  carry  the  power  to  the  manufactory,  instead  of  carrying  the 
manufactory  to  the  power,  which  was  necessarily  located  on  a  hill- 
side, where  the  wheel-pits  were  to  be  excavated. 

"  The  motors  were  a  pair  of  water-wheels,  24  feet  diameter  and  18 
feet  long,  with  a  fall  of  water  20  feet,  and  a  second  pair  of  water- 
wheels,  50  yards  above  them,  18  feet  diameter  and  19  feet  long, 
under  a  fall  of  16  feet. 

"A  small  shaft  only  3  inches  diameter,  if  revolving  with  200 
Rpm,  was  deemed  sufficient  to  transmit  all  the  power  of  the  upper 
pair  of  wheels ;  and  by  transmitting  this  power  to  another  lower  line 
of  shafting  of  the  same  size,  but  with  the  velocity  doubled  to  400 
Rpm,  it  was  also  deemed  sufficient  to  receive  the  additional  power  of 
one  of  the  lower  pair  of  24-feet  wheels.  A  driving  pulley  of  10  feet 


144  RULES    FOR    BELTING. 

diameter  on  the  upper  line  of  shafting  transmitted  the  power,  by  a 
belt  12  inches  wide  to  a  5-feet  pulley  on  the  lower  shaft,  to  its 
double  speed. 

"  This  idea  was  more  readily  conceived  than  executed.  The  move- 
ment of  a  pulley  of  the  dimensions  of  10  feet  diameter,  with  a  surface 
velocity  of  over  6000  Fpm,  had  never  before  been  attempted  prac- 
tically. Doubts  were  suggested  of  the  safety  of.  using  belts  with  this 
velocity  in  mills.  But  after  having  trusted  my  own  body  to  travel 
with  the  speed  of  a  mile  a  minute,  over  English  railways,  with 
numerous  other  passengers,  drawn  by  a  ponderous  locomotive  engine 
of  35  tons'  weight,  whirled  around  curves,  over  precipitous  embank- 
ments, and  uncertainly  fastened  rails,  it  seemed  very  rational  to 
trust  a  leather  belt  to  travel  with  the  same  speed.  Thus  reassured, 
the  doubter  might  smile  at  the  suggestion  of  danger  of  risking  a  light 
belt  to  journey  at  the  same  rate.  But  there  had  been  no  light  pul- 
leys made  suitable  for  this  use.  Those  previously  in  use,  made  of 
two  iron  rims,  covered  with  wooden  lags  bolted  thereto,  were  rejected 
as  unfit. 

"  Although  the  superior  convenience  of  belts  over  wheel-work  and 
shafting  for  transmitting  power  had  induced  many  attempts  to  use 
them  30  years  ago,  yet  the  experimenters  had  commonly  failed  of 
successfully  operating  them  with  the  low  rate  of  speed  then  used. 
Pulleys  had  not  been  made  sufficiently  light  and  well  balanced  for 
any  one  to  adventure  to  use  them  with  the  high  speed  required  for 
leather  belts  to  operate  advantageously.  With  the  slow  speed  it  was 
necessary  to  strain  the  belts  so  tightly  on  the  pulleys,  to  produce 
sufficient  adhesion,  without  slipping  around  on  the  smooth  surfaces, 
that  the  lacings  and  texture  of  the  leather  yielded ;  and  so  frequent 
repairs  were  required,  that  the  superintendents  of  mills  nearly  all 
abandoned  the  use  of  them  for  transmitting  the  power  from  the 
motors  to  the  mill  shafting.  They  fell  back  on  the  old  system  of 
slowly  revolving  heavy  shafting  and  wheels. 

"  To  carry  out  the  proposed  system  new  patterns  of  pulleys  were 
therefore  made.  The  first  pulley,  10  feet  diameter,  proved  to  be 
imperfect,  and,  when  tested  with  a  velocity  of  about  8500  Fpm,  the 
rim  soon  made  its  exit  through  the  roof  of  the  wheel-house,  and 
continued  its  course  in  a  parabolic  curve  through  the  air  several 
hundred  yards,  until  it  finally  transmitted  its  motive  power  to  plough 
a  furrow  in  a  meadow.  A  remodelled  pulley,  made  to  take  the 
place  of  the  wandering  one,  stood  the  test  and  has  continued  faithful, 
without  deserting  its  post,  to  perform  the  duty  assigned  to  it  ever 


RULES    FOR    BELTING.  145 

since,  during  a  period  of  16  years.  The  same  belt  has  also 
remained  in  use,  in  good  order,  after  travelling  about  a  quarter  of  a 
million  of  miles  every  year  in  its  daily  circuits,  with  a  velocity  of 
6000  Fpm. 

"  As  a  test  of  the  efficacy  of  this  small  3-inch  shaft  to  transmit 
the  power  from  3  water-wheels,  it  may  be  stated  that  not  a  single 
shaft  or  coupling  has  required  renewal  or  repairs,  and  they  appear 
still  capable  of  a  much  longer  service.  This  same  3-inch  shaft  has 
also  served  to  transmit  all  the  power  of  the  steam-engine  used  in 
times  of  drought. 

"  The  contrast  between  the  two  systems  of  high  an/i  low  rates  of 
speed  of  shafts  and  belts,  for  transmitting  power  from  motors  to 
manufactories,  is  instructively  exhibited  in  these  two  narrated  in- 
stances of  the  practical  application  of  each  of  them,  with  conclusive 
results  of  the  failure  of  the  latter. 

"  To  avoid  the  use  of  the  brittle  teeth  of  wheels,  quite  recently  the 
adhesion  by  friction  of  the  surfaces  of  wheels  has  been  employed  for 
the  transmission  of  power.  To  intensify  the  friction,  the  adhesion 
has  been  increased  by  turning  grooves  and  ridges  on  the  faces  of  the 
wheels  brought  together  by  pressure. 

"  This  arrangement  has  been  found  advantageous  for  engaging  and 
disengaging  heavy  washing  machines  and  other  apparatus  in  dye- 
houses  and  bleacheries,  where  leather  and  India-rubber  belts  fail. 

"  It  may  be  questioned  whether  there  is  not  a  great  loss  of  power 
by  transmission  through  a  length  of  300  feet  of  a  3-inch  shafting. 

"  Undoubtedly  some  power  is  lost  by  friction  in  this  case,  but  not 
so  much  as  by  the  massy  shafts  described,  or  by  a  similar  line  of 
main  shaftings  in  mills,  where  the  friction  is  much  augmented  by 
loading  the  shafts  with  numerous  pulleys,  and  by  the  tension  of 
numerous  belts. 

"  If  kept  in  line  and  properly  attended,  the  friction  of  a  naked 
shaft  of  the  length  of  300  feet  is  so  small  as  to  be  easily  turned  by 
the  hand  of  a  man.  The  friction  being  caused  by  the  weight  of  the 
shaft  only,  is  not  affected  by  any  extent  of  power  transmitted  by  it 
while  revolving,  whether  it  vary  from  one  to  an  hundred  horse-power. 

"  Where  high  velocities  of  mill  gearing  are  used,  it  is  desirable 
to  limit  any  accidental  extreme  acceleration  that  might  prove  inju- 
rious. 

"  This  was  readily  accomplished  by  the  simple  arrangement  of  a 
latch,  to  be  lifted  by  a  touch  of  the  whirling  arm  of  the  ball  regu- 
lator, whenever  the  accelerated  speed  causes  it  to  rise  to  a  certain 
10 


146  RULES    FOB    BELTING. 

prescribed  limit.  The  lifting  of  this  latch  disengages  the  connection 
of  the  regulator  with  the  gate  of  the  water-wheel,  arid  simultaneously 
engages  another  adjacent  revolving  wheel,  that  instantaneously  shuts 
the  gate  more  quickly  than  can  be  done  by  hand.  By  this  automatic 
action  the  water-wheel  itself  is  made  a  self-regulating  machine. 

"A  wire  extended  from  the  distant  mill,  like  a  bell-wire,  serves  to 
communicate  with  the  same  latch  by  a  slight  pull  of  the  hand,  and 
to  shut  the  gate  of  the  water-wheel  by  the  same  automatic  arrange- 
ment. This  was  devised  for  use  only  in  case  of  accident,  requiring 
the  immediate  stoppage  of  the  machinery. 

"This  same  system  should  be  applied  to  automatically  shutting 
off  steam  from  an  engine,  whenever  the  velocity  may  accidentally 
become  accelerated  beyond  a  prescribed  limit,  to  endanger  the 
machinery. 

"  The  very  important  advantage  of  combining  together  the  action 
of  the  several  motors  of  a  manufactory  to  co-operate  in  concert  for 
equalizing  the  regulation  of  the  speed  of  the  looms,  self-actors  and 
other  machines,  requiring  great  uniformity  of  movements,  is  really 
available,  where  the  velocity  of  a  mile  per  minute  of  a  connecting 
belt  is  adopted.  While  the  strongest  shafting  and  cog-wheels  fail  to 
accomplish  this  work,  even  with  the  most  massive  materials,  as  has 
been  described,  all  4  of  the  water-wheels  of  the  Georgia  mill  have 
been  very  satisfactorily  and  successfully  made  to  act  in  unison  by  a 
single  belt  of  only  8  inches  in  width.  This  belt  serves  to  transmit 
back  and  forth  between  the  motors  any  excess  of  power  that  either 
may  receive,  and  to  return  any  surplus,  to  an  extent  of  60  horse- 
power. A  range  of  variation  of  120  horse-power  is  thereby  available 
for  maintaining  an  equable  movement  of  all  the  machines  of  a  large 
manufactory  with  admirable  regularity.  The  elasticity  and  slight 
slipping  of  the  belts  relieves  the  shocks  of  more  than  100  tons  of 
water-wheels,  which  break  the  teeth  and  shafting  made  of  rigid, 
unyielding  iron. 

"  This  system  was  necessarily  introduced  to  prevent  the  waste  of 
water  that  ensues  when  two  mill  regulators  are  used  to  control  the 
flow  of  water  successively  from  one  pair  of  wheels  above  another 
lower  pair.  The  two  regulators  cannot  be  made  to  act  harmoniously, 
for  each  one  is  governed  by  the  varying  load  of  machinery  imposed 
on  each  motor.  The  annoying  waste  of  the  surplus  water  in  times 
of  drought,  shut  off  by  the  regulators,  and  flowing  past  without  use- 
ful effect,  can  be  prevented  entirely  by  using  only  one  regulator  oil 
the  upper  wheels  for  controlling  the  whole  of  the  machinery. 


RULES    FOR    BELTING.  147 

"  Thus  a  small  leather  belt,  of  only  8  inches  width,  has  been  suc- 
cessfully employed  for  many  years,  and  is  still  employed,  with  the 
velocity  of  a  mile  a  minute,  to  control  the  speed  of  4  water-wheels, 
like  leather  reins  to  bridle  4  steeds. 

"  In  a  manufactory  operated  by  two  independent  motors,  with  dis- 
tinct lines  of  shafting,  the  two  systems  may  be  connected  even  by  an 
inch  belt  moving  with  high  velocity,  to  modify,  wonderfully,  the 
sudden  extremes  of  speed,  so  disadvantageous  where  machines  are 
operated,  requiring  nice  adjustments  of  power." 

"  In  the  present  experimental  state  of  the  introduction  of  pulleys 
and  belts,  moving  with  high  velocities  for  the  transmission  of  power 
to  a  distance  from  motors,  a  few  facts  may  be  briefly  stated  to  inspire 
confidence  in  the  operators  of  mills  to  adopt  new  arrangements  by 
learning  what  has  been  found  practically  successful. 

"  A  good  leather  belt,  one  inch  wide,  has  sufficient  strength  to  lift 
1000  Ibs. 

"  The  speed  of  a  mile  per  minute  for  main  driving  leather  belts 
has  been  found  both  safe  and  advantageous  for  practical  use. 

"  The  capability  of  belts  to  transmit  power  is  determined  by  the 
extent  of  its  adhesion  to  the  surface  of  pulleys. 

"  The  extent  of  adhesion  of  belts  varies  greatly  under  varying  cir- 
cumstances of  the  use  of  them,  and  is  very  limited  in  comparison 
with  the  absolute  strength  of  the  leather. 

"The  adhesion  and  friction,  causing  the  belt  to  cling  to  the  surface 
of  a  pulley  without  slipping,  is  mainly  governed  by  the  weight  of 
the  leather,  if  used  horizontally. 

"  If  belts  are  strained  tightly  on  the  pulleys,  then  the  adhesion  is 
increased  in  proportion  to  the  increased  tension  produced. 

"  The  weight  of  leather  in  vertical  belts  tends  to  produce  a  sag 
beneath  the  under  side  of  the  under  pulley ;  and,  if  loosely  put  on, 
might  not  touch  it  at  all,  to  transmit  power  by  adhesion.  For  this 
reason  it  is  necessary  to  strain  on  more  tightly  all  vertical  belts,  with 
a  dependence  on  the  elastic  stretch  of  the  leather  for  producing  adhe- 
sion. 

"  A  vertical  belt  of  single  leather  of  the  width  of  6  inches,  and  with 
a  velocity  of  5200  Fpm,  has  practically  been  used  very  satisfactorily 
at  the  Georgia  mill,  during  several  years,  to  operate  10,400  self-act- 
ing mule-spindles,  and  the  spoolers  and  warpers  for  the  same ;  and 
another  belt  of  similar  width  and  velocity,  110  feet  in  length,  has 
served  to  transmit  the  power  from  a  24-feet  water-wheel,  18  feet  long, 
under  a  fall  of  20  feet,  with  the  same  velocity  of  5200  feet. 


148  KULES    FOR    BELTING. 

"A  24-inch  belt  of  single  leather,  with  the  velocity  of  4850  Fpm, 
has  transmitted  all  the  power  of  a  steam-engine  of  6-feet  stroke,  30- 
inch  cylinder,  making  40  Rpm,  and  with  so  slack  a  tension  on  the 
returning  side  as  to  flap  and  wave  with  an  undulating  movement. 

"These  statements  are  specified  simply  to  show  what  has  been  done 
by  belts  running  with  certain  velocities,  not  for  the  purpose  of  hold- 
ing them  up  as  models  for  imitation. 

"  No  fixed  rule  can  be  given  for  calculating  the  actual  adhesion 
of  belts ;  for  this  adhesion  depends  upon  so  many  contingent  facts  of 
their  relative  positions  and  weights,  as  affected  by  greater  or  less 
lengths  and  breadths,  and  lightness.  As  the  result  of  experimental 
observations,  it  may  safely  be  calculated  that,  with  a  properly  slack 
belt,  the  effective  adhesion  of  a  horizontal  belt  may  be  taken  at  30 
Ibs.  to  each  inch  of  width  of  short  belts,  and  double  of  this  on  long 
belts,  with  threefold  or  more  if  tightly  strained  on  the  pulleys,  which 
never  should  be  done,  for  this  increases  the  friction  of  the  bearings 
and  waste  of  power,  in  addition  to  injuring  the  durability  of  the 
leather  for  service. 

"  Clamps  with  powerful  screws  are  often  used  to  put  on  belts  with 
extreme  tightness  upon  the  pulleys,  and  with  most  injurious  strain 
upon  the  leather.  They  should  be  very  judiciously  used  for  horizon- 
tal belts,  which  should  be  allowed  sufficient  slackness  to  move  with 
a  loose  undulating  vibration  on  the  returning  side,  as  a  test  that  they 
have  no  more  strain  imposed  than  what  is  necessary  simply  to  trans- 
mit the  power. 

"  Rather  than  to  continue  to  use  horizontal  belts  with  overstrained 
tightness  to  obtain  the  necessary  adhesion,  it  is  often  better  to  use 
larger  pulleys,  which  require  less  adhesion  to  transmit  an  equal 
extent  of  power. 

"  On  the  scientific  principle  that  the  adhesion,  and  consequently 
the  capability,  of  leather  belts  to  transmit  power  from  motors  to 
machines,  is  in  proportion  to  the  pressure  of  the  actual  weight  of  the 
leather  on  the  surface  of  the  pulley,  it  is  manifest  that,  as  longer 
belts  have  more  weight  than  shorter  ones,  and  that  broader  belts  of 
the  same  length  have  more  weight  than  narrower  ones,  it  may  be 
adopted  as  a  rule  that  the  adhesion  and  capability  of  belts  to  trans- 
mit power  is  in  the  ratio  of  their  relative  lengths  and  breadths.  A 
belt  of  double  the  length  or  breadth  of  another,  under  the  same  cir- 
cumstances, will  be  found  capable  of  transmitting  double  the  power. 
For  this  reason  it  is  desirable  to  use  long  belts.  By  doubling  the 
velocity  of  the  same  belt,  its  effectual  capability  for  transmitting 
power  is  also  doubled." 


RULES    FOR    BELTING.  149 

From  Daniel  Hussey,  Lowell,  Mass.,  in  "  Proceedings  of  N.  E. 
Cotton  Manufacturers'  Association,"  No.  10,  April  19,  1871. 

98.  "  A  leather  strap  or  belt  an  inch  wide  will  sustain  1000  Ibs. 
before  breaking.  I  have,  therefore,  taken  8  per  cent,  of  the  breaking 
weight,  or  80  Ibs.  to  the  inch,  or  about  400  feet  to  the  horse-power, 
as  a  tension  that  will  not  materially  injure  the  leather  for  a  long 
period  by  overstraining  or  stretching.  This  is  used  for  single  belts 
—  main  drivers  only.  A  double  belt  will  give  J  more  equally  well. 

"  As  regards  the  velocity  of  belts,  this  subject  admits  of  a  wide 
margin.  Ordinarily,  counter-belts,  where  the  centres  are  not  more 
than  12  feet  apart,  will  require  1000  feet  to  horse-power  per  minute, 
and  card  and  loom  belts  from  2000  to  3000  horse-power  per  minute. 
When  at  the  Nashua  Co.'s  mills,  I  ran  a  20-inch  single  belt  7200  Fpm 
from  a  14-feet  diameter  to  a  4-feet  diameter  pulley,  which  ran  suc- 
cessfully on  the  14-feet  diameter,  but  the  centrifugal  force  on  the 
4-feet  diameter  pulley  caused  it  to  jump  or  fly  from  the  surface  and 
run  a  little  uneven,  owing  to  the  uneven  weight  and  thickness  of  the 
leather. 

"I  think  it  would  have  run  well  on  a  6-feet  diameter  pulley. 
When  it  was  running  6000  Fpm  it  ran  very  satisfactorily  indeed,  and 
I  could  not  have  asked  to  run  it  better.  From  this  experiment  I 
have  come  to  the  conclusion  that  6000  feet  is  as  fast  as  a  belt  should 
run  when  the  small  pulley  is  not  over  4  feet  diameter.  Taking  this  as 
a  basis  of  calculation,  a  10-feet  pulley  may  run  a  belt  10,000  Fpm 
with  safety.  It  is,  however,  seldom  in  practice  that  we  should  need 
such  quick  speed.  Some  three  weeks  since  I  commenced  running  a 
single  belt  5400  Fpm  —  the  smaller  pulley  being  about  4  feet  diam- 
eter— which  gives  excellent  satisfaction.  I  know  of  no  definite  rule 
for  running  belting;  everything  depends  upon  surrounding  cir- 
cumstances. 

"A  horizontal  belt,  running  on  not  less  than  a  7-feet  diameter 
pulley,  50  feet  from  centre  to  centre,  and  working  side  at  bottom, 
will  run  well  with  400  feet  to  a  horse-power,  the  slack  being  taken 
up  by  its  own  weight.  The  same  belt,  at  an  angle  of  45°,  will  require 
500  feet  to  the  horse-power,  and  with  a  vertical  belt  it  will  be  almost 
impossible  to  run  it  any  length  of  time  without  a  binder  (which,  of 
all  things,  we  most  dread  in  a  mill).  I  will  now  mention  one  law  of 
belting  that  may  not  be  known  to  you  all,  i.  e.,  the  hug  or  adhesion 
is  as  the  square  of  the  number  of  degrees  which  it  covers  on  the 
pulley,  or,  in  other  words,  a  belt  that  covers  |  of  the  circumference 


150  RULES    FOR    BELTING. 

of  a  pulley,  requires  4  times  the  power  to  make  it  slip  as  it  does 
when  it  covers  ^  of  the  same  pulley. 

"  Belts,  like  gears,  have  a  pitch-line,  or  a  circumference  of  uniform 
motion.  This  circumference  is  within  the  thickness  of  the  belt,  and 
must  be  considered  if  pulleys  differ  much  in  diameter  and  you  must 
get  a  required  speed. 

"  Owing  to  the  slip,  elasticity,  and  thickness  of  the  belt,  the  cir- 
cumference of  the  driven  seldom  runs  as  fast  as  the  driver.  With 
two  pulleys  of  equal  diameters,  one  may  be  made  to  run  twice  as 
fast  as  the  other  without  slipping,  if  you  use  an  elastic  belt  of  India- 
rubber. 

I  simply  mention  this  to  show  the  effect  of  elasticity  in  belts.  As 
the  power  of  a  belt  is  as  its  velocity,  it  is  well  to  run  it  as  fast  as 
possible  to  avoid  lateral  pressure,  and,  consequently,  friction  of  the 
shaft." 

Pulleys. 

"  One  of  the  greatest  objections  to  the  fast  running  of  shafting  and 
belts  is  the  want  of  pulleys  properly  constructed.  My  experience 
leads  me  to  the  conclusion  that  it  is  not  safe  to  run  a  cast-iron  pulley 
4  feet  diameter  400  Rpm,  owing  to  the  unequal  shrinkage  of  castings 
in  coaling  and  other  imperfections.  Running  slow,  the  centrifugal 
force  has  but  little  effect ;  but  as  the  centrifugal  force  is  as  the  square 
of  the  velocity,  it  is  not  so  easily  overcome  in  rapid  motions. 

"  If  you  make  the  rim  of  the  pulley  thicker,  the  centrifugal  force 
increases  with  the  thickness,  and,  consequently,  nothing  is  gained  by 
the  extra  iron.  I  have,  therefore,  substituted  white  pine  felloes 
made  of  one-inch  boards,  breaking  joints  for  the  rim,  built  on  cast- 
iron  hubs  and  arms.  The  centrifugal  force  of  material  is  as  the 
specific  gravity,  and  the  specific  gravity  of  cast-iron  is  13  times 
that  of  pine,  hence  the  centrifugal  force  must  be  13  times  greater ; 
but  the  tensile  strength  of  cast-iron  is  only  two  to  one  of  that  of 
pine,  therefore  the  rim  of  a  pulley  made  of  white  pine  felloes  will 
sustain  from  4  to  6  times  the  centrifugal  force  of  a  rim  made  of  cast- 
iron  ;  that  is,  the  same  diameter  with  white  pine  felloes  will  run  more 
than  double  the  velocity  without  being  torn  asunder.  It  is  less  likely 
to  be  broken  by  jar  or  blow,  and  is  less  than  half  the  weight,  and, 
of  course,  takes  less  power  to  run  it.  I  have  run  a  pulley  made  in 
this  way  16  feet  diameter,  4  feet  wide,  90  Rpm  for  18  months.  I 
have  just  started  another,  17  feet  diameter,  62  inches  wide,  100  Rpm, 
driving  on  to  one  made  the  same  way  4  feet  diameter,  and  running 
425  Rpm.  Both  of  these  are  working  well.  I  am  fully  convinced 


RULES    FOB    BELTING.  151 

that,  with  quick  shafting,  wood  must  take  the  place  of  cast-iron  for 
the  rims  of  pulleys  3  feet  diameter  and  above. 

"  No.  2  section  of  Lawrence  Manufacturing  Co.  has  been  running ' 
with  gears,  shafting,  pulleys,  and  belts,  conforming  as  nearly  as  pos- 
sible to  the  above  rules,  and  is  driving  the  shafting  for  38,000  spindles 
(throstle,  ring,  and  mule)  with  the  same  amount  of  power  as  it  for- 
merly required  for  19,000  spindles." 

From  LeffePs  "Mechanical  News." 

00»  "  But  not  only  have  band-saws  been  used  with  success  for 
heavy  work,  but  another  application  of  a  metallic  band  of  essentially 
the  same  nature  has  been  made,  and,  it  is  said,  with  satisfactory 
results.  We  refer  to  the  employment  of  a  belt  of  sheet-iron  instead 
of  leather  or  rubber  for  transmitting  power  from  one  pulley  to  another. 
This  has  been  done  in  at  least  one  instance  on  record  (see  Art.  146), 
and  the  operation  of  the  belt  is  reported  to  have  met  all  the  require- 
ments of  the  work.  The  pulleys  in  this  case  were  of  cast-iron ;  and 
it  is  suggested  that  if  pulleys  with  an  elastic  surface  were  employed, 
still  better  results  would  be  obtained.  The  substitution  of  steel  belts 
in  place  of  cast-iron  is  also  recommended  as,  at  least,  an  experiment 
worth  trying ;  and  the  fact  that  in  the  case  of  a  band-saw  the  saw 
itself  transmits  the  power  by  its  friction  on  the  lower  pulley.  As  high 
as  15  horse-power  being  in  some  cases  effectively  transmitted  by  such 
a  saw,  is  pointed  out  as  a  proof  of  the  entire  adaptability  of  steel  to 
belting  purposes. 

"  The  tensile  strength  of  low  steel  is  such  that  it  is  calculated  that 
a  belt  of  this  material  one  foot  wide  and  ^  inch  thick  could,  with  a 
safe  working  strain  ^—  the  same  in  proportion  to  actual  strength  which 
is  allowed  in  ordinary  belts  —  transmit  900  horse-power.  So  far  as 
ability  to  bear  tension  is  concerned,  this  is  certainly  enough  and  to 
spare.  (See  Art.  79.) 

"  The  various  mechanical  difficulties  which  may  suggest  themselves 
to  the  reader  as  liable  to  occur  have,  in  a  great  degree,  been  over- 
come in  the  manufacture  of  band-saws,  for  which  almost  precisely 
the  same  conditions  —  facility  of  joining  and  general  management — 
are  required  as  would  be  called  for  in  belting  for  any  class  of  work." 

The  following,  from  "  Overman's  Mechanics,"  1851, 

we  reproduce  here. 

100.  "  For  the  transmission  of  rotary  motion  belts  are  generally 
used ;  iron  chains  have  also  been  employed,  but  they  are  now  almost 


152  RULES    FOR    BELTING. 

universally  abandoned  for  wire  ropes.  If  an  India-rubber,  leather, 
or  any  other  description  of  belt  passes  around  a  pulley  it  adheres  to 
it  with  a  certain  force,  which  may  be  called  adhesion.  A  certain 
tension  of  belts  is  always  required  to  prevent  slippage ;  besides  which 
the  angle  of  contact  is  an  element  of  adhesion.  The  formula  for  the 
force  F,  which  is  to  be  transmitted  by  a  belt  of  the  tension,  t,  is : 

log.  F=  log.  t +  .434XC  x  ~, 

in  which  C  is  the  co-efficient  of  friction,  log.  the  common  logarithm, 
S  is  the  arc  of  the  pulley  covered  by  the  belt,  and  E  the  radius.  The 
common  co-efficient  of  friction  cannot  be  applied  in  this  case ;  it  is 
.47  for  greased  leather  upon  wood,  .50  for  dry  leather  upon  wood, 
.28  for  dry  leather  upon  cast-iron,  .38  for  oiled  leather  upon  cast-iron, 
and  .50  for  new  hempen  ropes  upon  wood.  India-rubber  belts  may 
be  classed  with  oiled  leather.  To  increase  the  arc  on  the  driving 
pulley,  that  which  is  driven  may  be  made  smaller,  and  to  increase 
the  arc  on  both  the  belt  may  be  crossed.  In  many  instances  the  arc 
as  well  as  the  tension  is  increased  by  a  tension  pulley. 

In  cases  where  all  these  are  insufficient  to  produce  the  adhesion 
required,  the  rope  may  be  put  around  the  pulley  more  than  once,  to 
afford  it  a  longer  time  of  contact.  This  is  particularly  resorted  to 
where  ropes  are  to  pull  heavy  loads,  as  up  inclined  planes.  This 
arrangement  is  here  represented  : 

If  the  pulley  A  is  grooved,  of  which  at  least  two  are  fastened  to 
the  same  shaft,  the  rope  is  directed  on  one  of  these  pulleys,  and, 
passing  around  it,  goes  to  B,  which  revolves  on  an  inclined  axis,  such 
that  the  rope  will  be  received  from  A'  and  delivered  to  A  in  the  plane 
of  the  grooves.  The  number  of  pulleys  may  be  multiplied  to  gain 
adhesion.  This  method  of  augmenting  friction  is  preferable  to  the 
tension  roller,  as  no  increase  of  tension  is  required ;  and  it  has  the 
additional  advantage  of  bending  the  rope  in  the  same  direction,  which 
makes  it  more  durable. 

To  determine  the  strength  and  size  of  a  belt,  find  first  the  amount 
of  labor  to  be  performed  by  it.  This  labor  is  its  tension  with  velocity. 

If  a  belt  passes  over  a  3-feet  pulley  which  makes  100  Rpm,  its 
velocity  will  be : 

100  x  3  x  3.1416  =  942.48  Fpm. 

If  this  belt  is  to  transmit  2  horse-power,  its  tension  on  the  pulling 
side  is :  2  X  33000 


942.48 


=  70  Ibs. 


RULES    FOR    BELTING. 


153 


In  this  case  it  is  assumed  that  one  side  of  the  belt  is  slack ;  if 
this  is  not  the  case, 
which  in  the  average 
of  practical  instances 
maybe  depended  upon, 
the  tension  on  the  fol- 
lowing side  of  the  belt 
is  subtracted  from  the 
above.  We  here  see 
of  how  much  more 
service  the  horizontal 
belt  is  than  the  ver- 
tical, for  it  increases 
the  tension  by  its  own 
weight,  and  also  the 


arc  of  contact. 


Fig.  18. 


In  most  of  these  cases,  we  may  neglect  the  width  of  the  pulley  in 
the  calculation  of  friction ;  for  the  strength  of  the  belt,  if  sufficient 
to  resist  the  tension,  makes  the  belt  wide  enough  for  adhesion.  In 
all  cases  it  is  advisable  to  make  the  belt  sufficiently  wide:  no  other 
loss  arises  from  too  wide  a  belt  than  that  of  first  cost  and  the  loss  in 
rigidity.  If  a  belt  is  too  narrow,  or  the  arc  of  contact  too  short,  the 
tension  must  be  increased,  in  order  to  afford  sufficient  adhesion  to 
the  pulleys. 

Short  belts  are  very  disadvantageous,  and  so  are  vertical  ones  : 
they  always  require  more  tension  than  either  long  or  horizontal 
belts.  Those  which  are  too  narrow  will  stretch,  in  consequence  of 
which  tension  and  adhesion  are  diminished.  The  adhesion  of 
leather  upon  iron  and  smooth  surfaces  is  greater  than  upon  wooden 
and  rough  surfaces ;  for  these  reasons  pulleys  ought  to  be  made  of 
iron,  and  perfectly  round  and  smooth.  Frequently  we  see  the  sur- 
face of  the  pulleys  convex,  in  order  to  prevent  the  running  off  of  the 
belt;  this  convexity  must  be  very  small,  or  it  will  diminish  adhesion. 
The  most  perfect  is  the  cylindrical  form  of  pulleys  for  flat  belts. 

Round  ropes,  or  strings,  are  conducted  by  grooved  pulleys,  in 
which  the  adhesion  of  the  rope  is  increased  by  the  wedge-form  of 
the  groove  into  which  it  is  squeezed ;  the  adhesion  of  these  ropes  to 
the  pulleys  increases,  therefore,  as  the  angle  of  the  groove  diminishes. 

Round  grooves  are  disadvantageous,  because  they  are  destructive 
to  the  rope,  caused  by  its  sliding  on  the  sides  of  the  groove.  The 
best  form  for  the  groove  is  angular,  so  that  the  rope  touches  but  in 
two  places  tangential  to  its  circumference. 


CHAPTER    II. 

METHODS  OP  TRANSMISSION  BY  BELTS  AND  PULLEYS. 

Main  Driving  Belts. 

101.  Mr.  S.  S.  Spencer,  Superintendent  of  Conestoga  Mills  Nos. 
'2  and  3,  at  Lancaster,  Pa.,  has  kindly  furnished  me  with  the  follow- 
ing particulars  of  the  main  driving  belts  now  in  use  in  these  two 
mills : 

Mill  No.  2  is  driven  by  a  horizontal  condensing  Corliss  engine, 
having  a  30-inch  cylinder,  6  feet  stroke,  and  running  52?  Rpm. 
The  fly-wheel  is  22  feet  in  diameter,  and  weighs  25  tons.  It  has 
teeth  on  its  periphery  of  5.183  inches  pitch,  18-inch  face,  and  drives 
a  "jack"  9  feet  1\  inches  diameter  on  a  counter-shaft  9  feet  10  inches 
below  the  engine  shaft.  On  this  counter-shaft  are  three  9-feet  6-inch 
pulleys,  each  driving  a  5-feet  pulley  on  the  main  lines  as  here  shown. 


Fig,  19. 

The  belts  running  to  right  and  left  are  each  23 £  inches  wide,  and 
each  transmits  125  horse-power.  The  middle  belt  is  29  inches  wide, 
and  transmits  175  horse-power.  All  are  of  double  leather. 

154 


METHODS    OF    TRANSMISSION.  155 

Mill  No.  3  is  driven  by  a  horizontal  non-condensing  Corliss  engine 
of  28-inch  cylinder  and  5-feet  stroke,  running  50^  Kpm,  having  a  22- 
feet  diameter  fly-wheel  pulley  of  17  tons'  weight. 

Two  14J-inch  double  leather  belts  on  the  fly-wheel  run  to  right  and 
left,  driving  7-feet  pulleys  on  the  line  shafts,  thus :  (Fig.  20.) 


Fig.  20. 

The  belts  transmit  250  horsepower,  have  been  in  use  since  1852, 
and  are  doing  well.  If  we  suppose  each  belt  does  half  the  work,  we 
will  have  33.64  square  feet  of  belt  in  motion  per  minute  per  horse- 
power. 

Another  case  worthy  of  note  is  that  of  a  16-inch  cylinder,  48-inch 
horizontal  Corliss  engine,  with  14-feet  diameter  fly-wheel  pulley, 
making  65  Rpm,  carrying  a  12-inch  double  leather  belt  over  a  5-feet 
pulley  on  the  line  shaft,  which  is  located  under  the  second  floor  of 
the  factory  in  the  usual  way,  and  3  7  feet  horizontally  distant  from 
the  engine  shaft.  This  engine  is  doing  90  horse-power,  and  has  been 
running  8  years.  The  velocity  of  belt  surface  here  is  2860  Fpm, 
and  gives  31.77  square  feet  of  belt  per  minute  per  horse-power. 

Mr.  Spencer  further  says :  "  Whether  a  belt  is  more  or  less  liable 
to  slip  on  the  larger  pulley,  I  say  less  in  all  cases.  There  is  great 
advantage  in  covering  the  smaller  pulley  with  leather  where  much 
work  is  required.  It  is  much  better  to  use  narrow  belts  and  pulleys 
of  large  diameter,  than  wide  belts  and  pulleys  of  small  diameter. 
This  fact  is  probably  less  understood  and  appreciated  than  any  other 
in  connection  with  belts  and  pulleys.  Belts  require  care  in  their 
application  and  management.  I  have  belts  that  have  been  in  use  22 
years  under  rather  unfavorable  circumstances,  and  look  to-day  (1872) 
as  if  they  would  last  10  years  longer." 


156  METHODS    OF    TRANSMISSION. 

Main  Driving  Belts. 

102*  Mr.  W.  B.  Le  Van  presents  this  and  the  next  case  of 
driving  belts  : — At  A.  Campbell  &  Co.'s  factory,  Manayunk,  Philada., 
the  motive  power  is  transmitted  by  3  belts  to  3  separate  line  shafts, 
as  shown  in  Fig.  21. 


Fig.  21. 

Belt  No.  1  to  the  upper  6-feet  pulley  is  17  inches  wide.  Belt  No. 
2  to  the  8-feet  pulley  beneath  is  21 1  inches  wide.  Belt  No.  3  to  the 
8-feet  pulley,  to  the  right  in  the  cut,  is  26^  inches  wide.  The  belts 
are  all  double  leather,  and  run  from  the  pulley  fly-wheel  on  the  engine 
shaft,  which  is  24  feet  diameter,  6  feet  width  of  face,  and  weighs,  with 
its  shaft,  43  tons.  The  engine  is  a  horizontal  Corliss,  with  30-inch 
cylinder,  5-feet  stroke,  making  52  Rpm,  driving  about  20,000  spindles 
and  the  usually  connected  machinery. 

In  Fig.  22  we  give  an  indicator  card  taken  from  this  engine  on 
March  2,  1874,  under  a  boiler  pressure  of  85  Ibs.  Scale  of  card  30 
Ibs.  to  the  inch ;  average  pressure  45.8  Ibs. ;  horse-power  exerted  by 
1  Ib.  of  pressure  11.14;  estimated  power  to  run  engine  only  16.71 : 
hence  we  have  (11.14  X  45.8) — 16.71  =  493.5  horse-power.  Some 
of  the  cards  ran  as  high  as  47  Ibs.  average  pressure.  The  average 
of  8  cards  was  456.74  horse-power. 


METHODS    OF    TRANSMISSION. 


157 


MAMAYUNJC 

PA 


AV&AAGt  PffESSVRf. 


Fig.  22. 

Example. 

103.  At  Great  Bend,  Indiana,  an    18-inch   cylinder,  48-inch 
stroke,  Corliss  engine,  under  90  pounds  of  steam,  at  65  Rpm,  trans- 
mits 190  horse-power  usually,  and  at  times  222  horse-power,  through 
the  medium  of  a  22-inch  single  leather  belt  over  a  12-feet  fly-wheel 
pulley,  to  a  42-inch  pulleyvon  the  line  shaft. 

This  belt  was  originally  24  inches  wide,  but  using  the  figures  above 
we  get  23.64  and  20.23  square  feet  of  belt  in  motion  per  minute  per 
horse-power  respectively.  This  is  the  hardest  worked  belt  of  any  yet 
noted. 

Belt  at  J.  &  J.  Hunter's  Print-Works,  Hestonville,  Philada. 

104.  A  5-ply  gum  belt,  24  inches  wide  and  79  feet  long,  runs 
on  the  two  pulleys  15  feet  2  inches  and  6  feet  6  inches  in  diameter, 
situated  as  shown  in  Fig.  23,  the  lower  fold  drawing. 

The  engine  has  a  20-inch  cylinder,  36-inch  stroke,  and  makes  56 
Rpm,  works  under  80  Ibs.  boiler  pressure  of  steam,  and  gives  off  60 
to  70  horse-power. 

The  centre  of  the  6-feet  6-inch  driven  pulley  is  5  feet  6  inches 
above,  and  17  feet  9  inches  horizontally  distant  from  the  centre  of 
the  engine  shaft. 

The  data  given  above  show  that  when  60  horse-power  are  trans- 
mitted by  this  belt,  there  are  88.97  square  feet  of  belt  travelling  per 
minute  per  horse-power,  and  that  when  70  horse-power  are  transmitted, 
76.26  square  feet  are  travelling  per  minute  per  horse-power. 


158  METHODS    OF    TRANSMISSION. 

This  case  is  interesting  as  showing  the  amount  of  power  a  belt  is 
capable  of  transmitting  when  adhesion  is  produced  on  the  pulleys 
by  its  own  weight.  At  the  time  these  dimensions  were  taken  the  belt 
folds  were  within  4  feet  of  each  other. 


Fig,  23. 

• 

Mr.  H.  W.  Curtis,  of  this  city,  furnishes  the  following  on  Main 

Driving  Belts. 

103.  "  We  have  at  our  works,  now  Hale,  Kilburn  &  Co.,  a  20- 
inch  single  leather  belt  167  feet  long,  having  a  3-.J  inch  single  leather 
belt  cemented  and  riveted  on  its  outside  face  at  either  edge,  and 
transmitting  the  power  of  a  20-inch  diameter,  48-inch  stroke,  hori- 
zontal Corliss  engine.  It  is  arranged  to  give  power  directly  to  3 
shafts,  each  in  a  separate  room,  from  which  the  power  is  further  con- 
veyed by  means  of  vertical  belts  to  the  other  parts  of  the  factory. 
The  lower  fold  of  this  belt  extends  from  the  fly-wheel  over  a  pulley 
4  feet  in  diameter  (see  cut  No.  24)  situated  28  feet  from  and  23  feet 
above  the  horizontal  line  of  the  engine. 

"The  upper  fold  is  carried  12  feet  3  inches  higher,  and  over  a 
pulley  3  feet  in  diameter,  situated  directly  above  the  4-feet  pulley. 

"  The  main  receiving  pulley  is  6  feet  diameter,  situated  in  an  adja- 
cent building,  48  feet  horizontally  distant,  having  its  centre  on  a  level 
with  that  of  the  4-feet  pulley. 

"  The  fly-wheel  is  18  feet  diameter,  and  runs  60  Rpm,  giving  a 
velocity  to  this  belt  of  3392  Fpm,  and  was  calculated  to  give  125 


METHODS    OF    TRANSMISSION. 


159 


horse-power  on  the  3  pulleys  collectively,  in  the  proportion  of  80  on 
the  6-feet  pulley,  24  on  the  4-feet  pulley,  and  21  on  the  3-feet  pulley, 

"  This  would  make  70.6  square  feet  of  belt  per  minute  per  horse- 
power on  the  6-feet  pulley,  235.55  square  feet  on  the  4-feet  pulley, 
and  292.2  square  feet  on  the  3-feet  pulley.  If  considered  as  a  27-inch 
belt,  it  would  be  working  at  61  square  feet  per  minute  per  horse- 
power. 

"  This  belt  has  worked  up  to  125  horse-power,  as  proven  by  indi- 
cator cards  taken  from  the  engine,  which  subjects  the  lower  or  draw- 


Fig.  24. 

ing  fold  of  the  belt  to  a  tensile  strain  of  1216  Ibs.,  or  45  Ibs.  per 
inch  of  width,  allowing  7  inches  for  3J-inch  strips,  making  the  belt 
equal  to  one  of  a  single  thickness  27  inches  wide. 

"This  belt  has  been  running  9  months;  its  upper  fold  is  very  slack, 
the  longest  span  is  50  feet  at  an  angle  of  45°,  having  a  sag  of  20  to 
24  inches,  and  it  has  given  entire  satisfaction  during  that  time.  We 
have  also  3  other  belts,  with  similar  strips  on  their  outer  faces. 
These  belts  were  all  tried  single  at  first,  but  would  not  do  the  work 
required  of  them.  The  first  is  20  inches  wide,  taking  power  from  a 
pulley  4  feet  in  diameter  to  one  3  feet  in  diameter,  situated  12  feet 


160  METHODS    OF    TRANSMISSION. 

10  inches  directly  above.  The  next  is  16  inches  wide,  taking  the 
greater  part  of  the  power  from  the  20-inch  belt  by  means  of  a  40-inch 
pulley  to  one  24  inches,  situated  12  feet  6  inches  directly  above. 
These  belts  were  put  on  at  the  same  time  as  the  main  belt,  and  after 
trying  them  5  days,  running  only  part  of  the  machinery,  and  that 
with  insufficient  power,  we  thought  it  best  to  try  the  strips.  The 
result  was  that  with  the  strips  they  have  driven  all  the  machinery 
connected  with  them,  giving  no  trouble  whatever,  and  have  not  been 
tightened  more  than  once  in  the  time  named  above. 

"  The  next  is  an  8-inch  belt  driving  a  pump,  the  piston  of  which 
is  4  inches  diameter,  12-inch  stroke,  is  double-acting,  and  makes  24 
strokes  per  minute.  The  pulley  on  the  crank  shaft  of  pump  is  22 
inches  diameter,  and  this  is  driven  by  a  7-inch  pulley,  situated  9  feet 
below,  and  5  feet  from  the  perpendicular  line  of  the  pump ;  both 
pulleys  are  covered  with  leather.  The  pump  lifts  water  12  feet, 
through  a  2^-inch  pipe,  and  forces  it  80  feet  more  of  vertical  height 
through  123  feet  of  2-inch  pipe.  A  single  leather  belt  8  inches  wide 
was  first  applied,  but  it  would  not  drive  the  pump  at  all.  It  was 
thoroughly  tried  by  being  drawn  so  tightly  that  it  parted  at  one  of 
the  splices  in  a  few  minutes.  It  was  then  provided  with  strips,  one 
on  each  edge  1^-inch  wide,  and  put  on  again,  driving  the  pump  suc- 
cessfully. It  runs  about  3  hours  each  day,  and  has  not  been  tight- 
ened in  5  months. 

"From  the  above  results  it  is  plain  to  see  that  our  experience  with 
belts  of  this  character  has  been  very  satisfactory  thus  far,  and  we  do 
think  that  belts  made  heavier  and  stronger  on  their  edges  conform 
to  the  convexity  of  pulleys  better,  and  that  the  same  weight  of  leather 
will  drive  more  and  keep  straighter  than  when  put  in  any  other  form. 
We  do  not,  however,  recommend  belts  strengthened  by  narrow  strips 
on  their  outer  faces  for  running  at  a  high  speed  over  very  small 
pulleys;  in  such  places,  only  light  belts,  of  an  even  thickness,  should 
be  used." 

Main  Driving  Belts. 

106.  Referring  to  Fig.  25,  which  represents  the  driving  arrange- 
ment of  the  "  Patent  Metal  Co.,"  Philada., 

A  is  a  12- feet  pulley,  18-inch  face,  running  55  Rpm. 
B     "       4     "        "        18    "        "          "     150      " 
C     "       6     "        "        32    "        "          "       50      " 
D     "       6  ft.  6  in.  "        32   "        "  "       46      " 

E    "      15-inch  single  leather  belt. 
F-   "     23     «     double     " 


METHODS    OF    TRANSMISSION.  161 

The  pulley  D  is  28  feet  from  A,  measuring  from  centre  to  centre 
of  shafts,  which  lie  in  the  same  level  plane,  and  B  is  24  feet  horizon- 
tally distant,  and  12  feet  above  A,  which  latter  is  a  heavy  main 
driving  pulley  on  the  engine  shaft.  The  cylinder  of  this  engine  is 
20  inches  diameter  and  36  inches  stroke,  the  fly-wheel  A  making  55 
Rpm.  Indications  taken  during  recent  trials  showed  that  105  horse- 
power were  transmitted  by  the  belt  F  to  the  pulley  D  on  the  roll 
shaft,  and  that  20  horse-power  were  transmitted  by  the  belt  E  to  the 
pulley  B  on  the  line  shaft.  During  one  trial  the  belt  F  was  found 
to  have  sufficient  adhesion  to  hold  the  engine  still  with  steam  on,  the 
amount  of  steam  admitted  to  the  cylinder  being  unequal  to  the  resist- 
ance at  the  rolls,  when  the  indicator  recorded  125  horse-power. 
Afterwards,  with  altered  valve  giving  later  point  of  cut-off,  this  same 
belt  drove  the  rolls  through  their  work  without  stoppage,  and  with 
an  average  indication  of  the  same  horse-power. 


Fig.  25. 

Means  of  Increasing  the  Adhesion  of  Belts. 

107.  Various  means  have  been  devised  for  augmenting  the 
adhesion  of  belts  to  the  pulleys  which  they  drive,  to  some  of  which 
we  now  refer.  With  the  ordinary  single  and  double  belts,  where  the 
usual  tightening  of  the  same  as  well  as  where  the  application  of  the 
several  oily  and  adhesive  matters  in  common  use  have  proven  insuf- 
ficient, a  very  simple  remedy  has  been  applied  with  success,  in  the 
shape  of  a  narrower  belt  drawn  tightly,  with  ends  laced  in  the  usual 
way,  and  allowed  to  run  with,  and  on  the  outside,  of  the  same. 

This  is  a  remedy  almost  too  simple  to  refer  to,  yet  it  has,  in  many 
11 


162  METHODS    OF    TRANSMISSION. 

instances,  proven  a  valuable  addition  to  the  driving  power  of  cer- 
tain belts  which  fail  to  transmit  the  power  desired  from  lack  of 
adhesion.  In  many  cases  belts  do  not  possess  sufficient  tensional 
strength  to  impart  the  power  due  to  their  surface  velocity ;  with 
such  the  auxiliary  belt  above  referred  to  is  the  cheapest  and  readiest 
cure. 

Double  leather  belts  are  frequently  employed  in  place  of  single 
ones,  to  increase  adhesion  on  the  pulley  surface ;  but  while  we  are 
assured  of  greater  tensional  strength  in  the  double  belt,  we  have  no 
data  to  prove  its  superior  adhesive  power. 

We  have,  however,  the  valuable  testimony  of  Mr.  F.  W.  Bacon,  of 
New  York,  whose  large  experience  in  this  line  of  practical  engineer- 
ing gives  weight  to  his  conclusions.  He  says :  "  I  never  use  double 
belts  under  any  circumstances.  I  am  satisfied  that,  other  things  being 
equal,  they  will  not  do  as  much  work  as  a  single  belt,  because  they 
do  not  come  in  contact  with  as  much  surface  as  the  more  pliable 
single  belts  do ;  hence  there  is  no  advantage  in  doubling  the  thickness. 
If  greater  tensional  strength  is  required  use  wider  belts." 

In  Fig.  26  we  present  the  "traction  gearing"  of  Mr.  Alonzo 
Hitchcock,  of  New  York,  which  consists  of 
3  pulleys,  each  on  an  axis  of  its  own,  and 
a  driving  belt  so  placed  that  the  driving 
pulley,  A,  touches  the  driven  pulley,  C.  These 
two  are  forced  into  close  contact  by  the  auxil- 
iary pulley  B,  over  which  the  belt  is  tightly 
Fig.  26.  drawn  from  the  pulley  A.  The  larger  pulleys 

may   be   leather   covered,  and  all  should  be 

straight  on  the  face  and  have  their  centres  in  the  same  straight  line, 
and,  of  course,  their  axes  in  the  same  plane. 

It  is  evident,  on  inspection,  that  the  belt  and  pulley  surfaces  all 
favor  rotary  motion  in  the  pulley  C,  and  while  the  pulleys  A  and  C 
may  vary  greatly  in  diameter,  producing  rapid  increase  of  speed, 
the  belt  passes  freely  and  with  full  driving  effect  over  comparatively 
large  pulleys.  The  pulley  B  being  made  of  any  diameter  desired. 

This  combination  was  patented  January  30,  1867.  The  inventor 
says :  "  I  claim  distributing  the  power  around  the  shaft  to  be  driven, 
so  that  the  tendency  to  displace  the  shaft  on  one  side  is  counteracted 
by  that  on  the  other,  by  the  means  and  in  the  manner  shown." 

A  more  complicated  arrangement  of  pulleys  for  gaining  a  high 
speed  of  rotation  at  once,  without  intermediate  pulleys,  is  shown  by 
Parker's  patent  belting  in  Fig.  27. 


METHODS    OF    TRANSMISSION.  163 

In  this  the  auxiliary  pulley,  B,  is  connected  to  the  driven  pulley,  C, 
by  an  endless  belt,  F  F,  but,  unlike  the  usual 
method,  the  driving  pulley  A  is  set  against  the 
outside  of  the  belt  to  contact  with  B  and  C,  the 
belt  passing  between. 

The  axis  of  the  pulley  B  turns  in  the  ends  of 
the  arms,  E,  one  being  on  each  side,  which  are 
jointed  with  the  arms  D  at  H,  outside  the  ^H>-  27. 

pulley;    the   other   ends   of  D  turn  upon  the  shaft  bearings  of 
pulley  A. 

These  levers  form  a  toggle  by  which  the  auxiliary  pulley  is  forced 
against  the  driving  pulley.  The  effect  of  this  combination  is  to  draw 
belt  and  pulleys  into  close  driving  contact,  and  at  the  same  time  to 
avoid  severe  lateral  strains  on  the  shaft  bearings. 

The  driving  and  driven  pulleys  may  have  diameters  of  30  to  40, 
and  even  as  high  as  50  to  1  respectively ;  the  driven  pulley  may, 
indeed,  be  nothing  more  than  an  enlargement  of  its  shaft,  and  the 
auxiliary  pulley  must  be  of  such  diameter  as  will  prevent  contact  of 
belt  at  F. 

The  pulley  surfaces  must  all  be  straight ;  that  of  C  may  be 
covered  with  leather,  the  belt  must  be  made  of  well  stretched 
leather  of  uniform  texture,  must  have  a  permanent  joint,  and  be 
of  equal  thickness  throughout  its  entire  length,  and  all  the  parts 
must  be  fitted  with  great  exactness  to  insure  perfect  working  of  the 
combination. 

Many  of  these  have  been  made  and  used  for  driving  small  circular 
saws,  where  hand-power  is  employed,  and  for  such  and  like  purposes 
they  answer  very  well. 

One  of  the  simplest  methods  of  increasing  the  efficiency  of  any 
belt  or  cord  is  with  pulleys  of  given  dimensions,  to  cause  it  to 
embrace  a  greater  portion  of  their  circumference,  which  increases 
proportionally  its  adhesion  as  well  as  its  driving  power.  The  fol- 
lowing shows  one  method  of  doing  this  by  the  cord  and  pulley 
arrangement. 

In  Fig.  28  one  fold  of  the  cord  is  drawn  out  of 
its  direct  course  between  the  peripheries  of  the 
driving  sheave  A  and  driven  sheave  C,  across  the 
other  fold  and  around  a  tightening  sheave,  B, 
which  is  so  arranged  as  to  be  moved  to  and 
from  the  other  sheaves,  and  set  at  such  an  angle 
as  to  prevent  contact  of  cords  at  points  of  cross-  Fig  28. 


164 


METHODS    OF    TRANSMISSION. 


Fig.  29. 


ing.  The  movement  of  B  is  such  as  to  permit  the  cord  to  run  in 
grooves  of  different  diameters  on  A  and  C,  by  which  different  speeds 
in  C  can  be  obtained  when  that  of  A  is  uniform. 

This  is  an  old  device,  and  is  frequently  applied  to  the  driving  gear 
of  foot-lathes. 

In  this  the  driving  power  is  limited  to  the  adhesion  of  the  single 
cord  in  the  sheave  grooves,  but  its  circumferential  contact  is  such  as 
to  give  the  greatest  effect  possible. 

In  order  to  greatly  increase  the  adhesion  of  the  cord  the  plan 
shown  in  Figs.  29  and  30  has  been  devised, 
and  consists  of  two  multigrooved  wheels, 
A  and  C,  the  driving  and  driven  sheaves 
of  the  system.  Into  the  grooves  of  these 
sheaves  is  wound  continuously  a  single  end- 
less cord,  in  parallel  lines  from  one  sheave 
to  the  other,  such  that  the  cord  in  leaving 
the  last  groove  of  A  is  deflected  across  and 
above  the  other  cords,  and  delivered  in  line 
of  the  groove  in  C  by  the  adjustable  single 
grooved  sheaves  B  and  B. 

The  bearings  of  these  sheaves   are  se- 
cured to  rods,  D  D,  fixed  parallel  with  the 
cords,  and  upon  which  the  sheaves  can  be 
slipped  and  fastened  to  take  up  slack  of  cord. 

It  is  evident  that  with  any  cord  its  adhesion,  and  consequently  its 
driving  power,  is  increased  in  the  direct  proportion  of  the  number  of 
grooves  in  each  driving  sheave. 

Referring  generally  to  pulleys  with  angular  grooves  for  round 
cords  of  any  material,  we  quote  from  Publication  Industrielle,  par 
Armengaud  aine,  Vol.  IX.,  p.  428  : 

"  This  system  is  much  in  use  for  transmitting  power  by  means  of 
hemp  cords  or  round  gut  belts  of  small  dimensions.  The  angular 
shape  of  the  groove  is  preferred,  in  order  to  increase  the  adhesion  of 
the  cord,  which  is  thus  pinched  between  the  surfaces  of  the  groove  by 
the  primitive  tension  it  receives  similar  to  ordinary  belts.  The  angle 
which  the  two  surfaces  form  with  each  other  is  made  ordinarily  60°." 
A  very  simple  method  of  driving  two  pulleys  on  separate  shafts 
from  one  pulley  is  shown  in  Fig.  31.  The  driving  pulley  A  has  a 
belt  running  to  B,  which  it  turns  in  the  usual  way. 

The  pulley  C  may  be  driven  by  A  also,  by  simply  running  its  belt 
over  the  belt  which  turns  B. 


Fig.  30. 


METHODS    OF    TRANSMISSION. 


165 


Fig.  31. 


The  belts  atop  of  each  other  on  A  increase  the  adhesion  sufficiently 
to  drive  both  B  and  C. 

We  have  found  it  convenient,  as  well  as  economical,  to 
resort  to  this  expedient  for  driving  lines  of  shafting  in  dif- 
ferent stories  from  the  prime  mover  below. 

"  Where  pulleys  of  very  unequal  diameter  are  coupled 
by  a  belt,  the  surface  of  contact  with  the  smaller  pulley  is 
so  little  that  the  belt  must  be  very  tightly  stretched,  in 
order  to  transmit  its  full  duty.  This  is  especially  the  case 
where  the  two  pulleys  are  very  near  each  other.  In  the 
case  of  the  small  centrifugal  pumps,  made  by  Gwynne  & 
Co.  for  plantation  and  farm  use,  the  horse  gear  is  con- 
nected with  the  pump  by  belting  from  a  large  pulley  to 
the  riggers  of  the  pump,  the  relative  diameters  of  the  two 
being  about  as  6:1,  while  also  they  are  placed  but  four  or  five 
inches  apart.  The  short  belt,  thus  acting  upon  a  very  small  portion 
of  the  surface  of  the  rigger,  requires  to  be  very  tightly  stretched, 
and  in  this  way  a  heavy  strain  is  brought  upon  the  bearings.  To 
relieve  this  strain,  Messrs.  Gwynne  &  Co.  place  a  friction  wheel 
between  the  pulley  and  rigger,  so  as  to  touch  both  in  a  line  connect- 
ing their  centres.  This  wheel,  revolving  freely  upon  a  fixed  centre, 
receives  the  strain  exerted  by  the  belt.  No  means  of  adjust- 
ment are  provided  to  compensate  for  the 
wear  of  the  journals,  nor  is  such  pro- 
vision believed  to  be  necessary.  The  ar- 
rangement, so  simple  in  itself,  appears  to 
possess  a  considerable  advantage  over  the 
ordinary  practice  of  throwing  the  whole 
strain  of  the  belt  upon  the  bearings." 

The   intermediate  pulley  is  recessed  in 
the  centre  of  its  face,  so  as  to  bear  on  the 


Fig.  32. 


others  at  the  edges  only, 
is  here  shown  (Fig.  32). 


The  arrangement  is  said  to  work  well,  and 


Double  Separate  Belts. 

108»  Mr.  J.  S.  Lever,  of  Philadelphia,  presents  this  curious  per- 
formance of  a  pair  of  belts,  shown  in  Fig.  33. 

"  The  driving  pulley,  a,  on  the  engine-shaft  is  5  feet  diameter,  and 
runs  75  Rpm ;  the  driven  pulley,  6,  on  the  line-shaft  is  3  feet  diam- 
eter, and  about  20  feet  distant  in  a  line  near  45°  with  the  horizontal. 
Both  pulleys  are  wooden  drums  covered  with  leather,  and  have  suf- 


166  METHODS    OF    TRANSMISSION. 

ficient  breadth  of  face  for  two  12-inch  belts.     When  this  arrange- 
ment was  started  two  12-inch  single  leather  belts  were  put  on  side 

by  side,  and  for  some 
time  were  run  in  that 
way,  but  never  satisfac- 
torily. After  many  fruit- 
less efforts  to  obtain  a 
uniform  action  of  the 
two  belts,  one  accident- 
ally mounted  the  other, 
the  two  running  thence- 
forth as  one  double 
belt.  In  this  way  they 
drove  the  line  -  shaft 
better  than  ever  before. 
Many  experiments 
were  tried  in  the  rela- 
tive tightness  of  the 

pi-      go  two  belts,  which  inva- 

riably proved  that  the 
best  driving  was  always  secured  when  the  inside  belt,  d,  was  very 
slack,  sagging,  say  12  to  18  inches,  and  the  outside  belt,  c,  quite  tight, 
the  working  sides,  of  course,  running  close  to  each  other,  as  shown 
in  the  cut.  This  was  in  use  some  thirty  years  ago  in  a  factory  near 
this  city." 

Imparting  and  Arresting  Motion. 

109.  Mr.  Thomas  Shaw's  dead-stroke  power-hammer  illustrates 
the  application  of  the  belt  for  giving  to  and  taking  motion  from  a 
shaft  at  the  pleasure  of  the  operator  (see  Fig.  34).  The  same 
devices  can,  however,  by  an  easy  transition,  be  applied  to  other 
machines. 

In  this  the  driving  pulley,  carrying  a  loose  belt,  is  on  a  line-shaft 
over  the  driven  flanged  pulley,  which  latter  is  on  a  shaft  at  the  top 
of  the  hammer-frame.  This  shaft  carries  a  crank-wheel  actuating  the 
hammer,  as  shown,  and  is  partly  invested  by  a  leather  band  for  arrest- 
ing its  motion.  One  end  of  this  band  is  secured  to  a  pin  in  the  hammer- 
frame  under  the  crank-wheel ;  the  other  end  is  fastened  to  the  swinging 
lever,  to  which  also  the  tightener-pulley  of  the  driving  belt  is  applied. 
The  action  of  these  belts  is  produced  by  opposite  motions  of  the 
lever ;  thus,  when  the  operator  pushes  it,  the  arresting-band  releases 
the  crank-wheel,  and  the  tightener-pulley  presses  upon  the  driving 


METHODS    OF    TRANSMISSION. 


167 


belt,  which,  being  constantly  in  motion,  applies  its  adhesion  to  the 
pulley  on  the  crank-shaft  and  propels  the  hammer ;  and  it  does  this 
with  a  varying  velocity,  according  to  the  pressure  upon  the  tightener. 
Withdrawing  the  lever  relaxes  the  driving  belt  and  tightens  the 


Fig.  34. 

arresting-band.  These  motions  are  under  the  easy  control  of  the 
operator,  and  such  is  the  nature  and  action  of  the  belt  in  this  appli- 
cation, that  these  motions  can  be  repeated  rapidly  and  effectively 
without  destructive  wear  to  any  part  of  the  machine. 


168  METHODS    OF    TRANSMISSION. 

Combined  Fast  and  Loose  Pulley  for  Round  Belts,  by  John  Shinn, 
of  Philadelphia. 

110.  The  round  belt,  /,  fits  in  a  groove  formed  between  two  half- 
pulleys,  of  which  A'  is  fixed  and  A  slides  upon  a  fixed  key  on  the  shaft, 
B ;  between  A'  and  A,  and  running  loosely  on  the  shaft,  is  a  flat-faced 
pulley,  C.  When  A  is  separated  from  A'  a  short  distance,  the  belt, 
/,  will  cease  to  turn  them,  and  will  run  on  and  turn  C  instead.  The 
belt  drives  the  shaft,  B,  only  when  pinched  between  the  half-grooves 


Fig.  35. 


of  A'  and  A.  The  lever,  D,  when  moved  in  the  direction  indicated 
by  the  arrow,  withdraws  the  half-sheave,  A,  and  permits  the  belt  to 
run  on  the  loose  pulley.  Simple  and  efficient  means  for  holding  the 
parts  together  and  drawing  one  half  from  the  other  are  shown  in 
the  cuts. 

It  is  not  proposed,  of  course,  to  drive  very  large  and  heavy  ma- 
chinery with  round  belts,  such  as  are  required  for  this  description 


METHODS    OF    TRANSMISSION. 


169 


of  shifting  pulleys;  but,  as  far  as  a  round  belt  will  go  with  advan- 
tage, these  pulleys  will  be  found  of  the  greatest  service.  Thus,  the 
round  belt  cuts  off  less 
light,  occupies  less  room, 
makes  smaller  holes  in 
the  floors,  needs  lighter 
driving  pulleys  to  carry 
it,  and  thus  saves  power ; 
while,  as  regards  the 
driving  power  of  round 
belts,  we  have  seen  one 
of  an  inch  diameter 
doing  for  years  work 
which  proved  too  much 
for  a  7-inch  flat  belt. 

Band  Links. 

111.  "  Where  ten- 
sion alone,  and  not 
thrust,  is  to  act  along 
a  link,  it  may  be  flex- 
ible, and  may  consist 
either  of  a  single  baud 
or  of  an  endless  band 
passing  round  a  pair  of  pulleys  which  turn  round  axes  traversing 
and  moving  with  the  connected  points.  For  example,  in  Fig.  37,  A 
is  the  axis  of  a  rotating  shaft.  B  that  of  a  crank-pin.  C  the  other 
connected  point,  and  B  C  the  line  of  connection  ;  and  the  connec- 
tion is  effected  by  means  of  an  endless  band  passing  around  a  pulley 
which  is  centred  upon  C,  and  round  the  crank-pin  itself,  which  acts 
as  another  pulley.  The  pulleys  are  of  course  secondary  pieces,  and 
the  motion  of  each  of  them  belongs  to  the  subject  of  aggregate 
combinations,  being  compounded  of  the  motion  which  they  have 
along  with  the  line  of  connection,  B  C,  and  of  their  respective  rota- 
tions relatively  to  that  line  as  their  line  of  centres ;  but  the  motion 
of  the  points  B  and  C  is  the  same  as  if  B  C  were  a  rigid  link,  pro- 
vided that  forces  act  which  keep  the  band  always  in  a  state  of 
tension. 

"  This  combination  is  used  in  order  to  lessen  the  friction,  as  com- 
pared with  that  which  takes  place  between  a  rigid  link  and  a  pair 


170 


METHODS    OP    TRANSMISSION. 


of  pins  ;  and  the  band  employed  is  often  of  leather,  because  of  'its 

flexibility."  —  Rankings  Mill  Work,  p.  218. 

In  Fig.  38  we  give  a 
substitute  for  Fig.  37, 
in  which  an  eccentric, 
B,  takes  the  place  of 
the  crank,  allowing  a 
straight  shaft  to  be  used. 
When  the  eccentricity 
of  B  equals  the  radius 
of  the  crank,  the  result 
is  the  same,  but  experi- 
ment has  proven,  in  the 
case  of  the  eccentric  used 

in  the  treadle  arranSe- 
ment  of  the  latter,  that 

the  motion  lacks  freedom,  the  treadle  moving  heavily. 


38 


Weaver's  Belting. 

112.  The  object  of  this  arrangement  is  to  obtain  high  speed  in 
a  shaft  directly  from  a  driving  pulley  without  the  aid  of  intermediate 
counter  pulleys  or  gears,  and  with  reduced  lateral  stress  on  the  bear- 
ings of  the  driven  shaft. 

A,  B,  and  C,  Fig.  39,  show  3  shafts  parallel  to  one  another.  A 
and  C  carry  straight-faced  pulleys,  upon  which  run  2  belts  of  equal 
length  and  width,  separated  to  prevent  contact  with  each  other  while 
running.  The  lower  fold  of  belt,  D,  is  carried  over  the  shaft,  B,  and 
the  upper  fold  of  belt  E  is  carried  under  B,  and  each,  in  running, 
imparts  motion  to  the  driven  shaft  in  the  same  direction,  and  at  the 
same  time  balancing  the  lateral  pressure  on  its  journals. 

A  is  the  driving  shaft  with  large  pulley  ;  B  the  driven  shaft  of 
comparatively  small  diameter,  and  C,  a  counter  shaft,  with  its  pulley 
of  any  convenient  diameter,  is  placed  in  position  to  carry  and  return 
the  belts,  and  may  be  moved  and  secured  to  and  from  B  by  screw 
adjustment  or  otherwise,  to  secure  proper  tension  of  belts. 


Belt  as  a  Friction  Clutch. 

113.  The  belt  offers  a  simple  and  efficient  means  of  producing 
intermittent  effects,  as  in  that  of  operating  stamps,  when  it  is  desira- 
ble to  control  by  the  hand  the  number  of  blows  in  a  given  time,  as 


METHODS    OF    TRANSMISSION. 


171 


well  as  to  vary  the  intensity  of  the  same  at  will.     Arranged  in  this 
manner  it  acts  as  a  friction  clutch. 


Fig.  39. 

In  Fig.  40,  the  shaft  J,  which  may  be  the  "  main  line  "  of  the  shop, 
or  a  counter  shaft,  carries  a  flanged  pulley,  H, 
continuously  revolving  in  the  direction  of  the 
arrow.  Over  this  pulley  is  thrown  loosely  a 
belt,  D,  one  end  of  which  is  fastened  to  the 
stamping  weight,  A,  at  E,  and  the  other  end  is 
secured  to  the  floor  at  F. 

The  weight,  A,  is  guided  in  the  parallel  up- 
rights, B  B,  and  rests  upon  the  base,  C.  As  the 
apparatus  stands,  the  weight  A  is  not  lifted, 
owing  to  slackness  of  the  belt,  but  by  taking 
hold  of  the  belt  at  G  by  the  hand,  and  drawing 
it  forcibly  in  a  horizontal  direction  and  at  right 
angles  to  the  shaft,  a  severe  tension  is  created 
in  the  belt  on  the  pulley,  which  latter  lifts  the 
weight  at  a  velocity  nearly  equal  to  that  of  F"  40 

its  rim.     Kelaxing  the  pull  on  G  lessens  the 
tension,  when  the  weight  falls  freely  back  to  the  base. 


172  METHODS    OF    TRANSMISSION. 

It  is  evident  that  the  number  of  blows  struck  may  be  repeated  at 
will,  and  that  the  force  of  the  blows,  in  so  far  as  they  may  be  due  to 
the  height  of  the  fall,  may  also  be  regulated  by  the  duration  of  the 
lateral  pull  on  the  belt. 

Since  the  effect  of  the  lateral  pull  on  G  is  as  G  F  -f  G  H,  and 
becomes  less  as  it  leaves  the  straight  line  joining  H  and  F,  it  is 
important  to  make  the  distance  H  F  as  great  as  may  be  convenient, 
and  to  keep  the  belt  as  taut  as  can  be  without  destructive  friction  on 
it  at  the  pulley  surface  when  not  in  use. 

For  the  lighter  hand-stamping  operations,  this  is  a  simple,  cheap, 
and  ready  means  of  obtaining  gravity  effects  on  dies  and  moulds. 

Nine  Dispositions  of  the  Quarter-Twist  Belt. 

The  Shafts  at  Right  Angles  but  not  in  the  same  Plane,  the  Belt 
Running  on  Two  Pulleys. 

114*  When  two  shafts  are  at  or  nearly  at  right  angles  with  each 
other,  and  not  in  the  same  plane  (Fig.  41),  and  it  is  desired  to  drive 
one  from  the  other  by  two  pulleys  only  and  a  connecting  belt,  expe- 
rience has  proved  that  certain  conditions  are  necessary.  In  the  first 
place,  the  distance  between  the  near  faces  of  the  pulleys  must  not  be 
less  than  four  times  the  width  of  the  belt.  The  pulleys  A  and  B 
should  be  so  placed  that  the  belt  will  lead  from  the  face  of  one  to 
the  centre  of  the  face  of  the  other,  that  is,  so  that  a  plane  passing 
through  the  centre  of  the  face  of  one  pulley  will  be  tangent  to  that  part 
of  the  face  of  the  other  from  which  the  belt  is  running. 

The  following  diagram  gives  the  position  and  proper  proportions 
referred  to : 


Fig.  41. 


METHODS    OF    TRANSMISSION. 


173 


The  pulley  A,  from  which  the  belt  deflects,  should  have  a  wider 
face  than  B,  in  the  proportion  of  10  to  6,  and  should  be  more  round- 
ing on  the  face  than  is  usual,  and  the  pulleys  should  be  as  small  as 
may  be  to  do  the  work,  and  should  be  of  nearly  equal  size. 

About  25  per  cent,  of  belt  contact  is  lost  when  the  belt  makes  a 
quarter-turn,  even  when  the  pulleys  are  of  the  same  size.  We  have 
noticed  in  the  performance  of  a  leather  belt  that  the  first  90°  of  lap 
on  the  pulley  fit  closely  as  in  the  ordinary  straight  belt  arrangement; 
but  in  the  second  90°,  about  half  the  width  of  the  belt  is  forced  from 
contact  with  the  pulley  by  the  strain  in  the  substance  of  the  belt,  due 
chiefly  to  its  imperfect  elasticity,  and  primarily  to  the  oblique  deflec- 
tion of  the  fold  which  is  leaving  the  pulley. 

With  a  belt  perfectly  elastic  the  same  amount  of  contact,  if  not 
more,  can  be  obtained,  as  with  the  open  belt,  since  the  belt  would 
adhere  to  the  face  of  the  pulley  up  to  the  line  of  departure  the  same 
in  one  case  as  in  the  other. 

A  Quarter-Twist  Belt. 
115.     Mr.  L.  H.  Berry,  of 

the  Atlantic  Works,  Philadel- 
phia, gives  the  particulars  of  a 
quarter-twist  belt,  arranged  by 
him,  and  shown  in  Fig.  42,  for 
driving  a  54-inch  circular  saw, 
the  periphery  of  which  travels 
at  the  rate  of  8400  Fpm,  and 
the  mandrel  lying  at  right  an- 
gles to  the  driving-shaft. 

"  On  the  mandrel  is  a  12-inch 
pulley,  and  on  the  driving-shaft, 
which  runs  horizontally  8  feet 
above,  is  a  wooden  drum  24 
inches  diameter,  8^  feet  long, 
upon  which  the  belt— a  10-inch 
heavy  single  leather,  travelling 
1800  Fpm — traverses  back  and 
forth,  following  the  reciprocat- 
ing movement  of  the  saw  man- 
drel. The  forward  movement 
of  the  saw  when  cutting  is  at 
the  rate  of  60  Fpm,  and  the  return  movement  120  Fpm. 


Fig.  42. 


174 


METHODS    OF    TRANSMISSION. 


"  From  some  cause  (centrifugal  force,  perhaps,  or  because  the  belt 
was  new,  and,  therefore,  not  as  pliable  as  it  would  otherwise  have 
been)  the  centre  of  the  pulley  had  to  be  set  8  inches  out  of  the  path 
of  the  vertical  line  from  the  periphery  of  the  drum.  (See  cut.)" 

The  Shafts  at  Right  Angles  but  not  in  the  same  Plane, 
the  Belt  Running  on  three  Pulleys.      Figs.  43  and  44. 

116*  A.  is  the  driving  pulley  on  a  horizontal  shaft ;  B  the  driven 
pulley  on  a  mill-spindle  or  upright  shaft ;  C  the  tightener  or  guide 
pulley,  which  is  placed  at  the  proper  angle  for  receiving  the  belt  from 
B  and  delivering  it  to  A.  It  has  a  short  shaft  running  in  bearings 
secured  to  a  frame  which  slides  vertically  in  fixed  grooves,  and  may 


Fig.  43. 

be  raised  to  tighten  the  belt  for  driving,  or  lowered  to  slacken  the 
belt  for  stopping,  B,  at  pleasure.  B  is  made  wide  and  straight  on  the 
face  to  admit  of  motion  in  raising  and  lowering  the  stones,  as  well  as 
to  allow  of  lead  of  belt  by  the  different  positions  of  C,  which  are 
due  to  length  and  tightness  of  belt. 

A  and  C  should  be  rounding  on  their  faces.     The  cut  shows  the 
proper  positions  of  the  pulleys  and  shafts,  and  also  gives  good  work- 


Fig.  44. 

ing  proportions,  the  particulars  having  been  obtained  from  machinery 
in  use ;  but  the  motion  of  the  belt,  as  shown,  should  be  reversed. 
The  quarter-twist  belt,  with  intermediate  guide  pulley,  like  Figs. 


METHODS    OF    TRANSMISSION. 


175 


43  and  44,  will  permit  of  very  short  distance  between  the  driving 
and  driven  shafts.  A  case  in  practice  may  be  cited,  in  which  the 
driving  pulley  is  40  inches,  the  driven  pulley  18  inches,  and  the 
guide  pulley  16  inches  in  diameter ;  all  of  them  are  8  inches  face, 
and  the  shafts  are  4  feet  7  inches  from  centre  to  centre,  vertically. 

This  distance  might  be  even  less  without  injury  to  the  belt.  In 
the  erection  of  this  arrangement  it  was  found  necessary  to  set  the 
face  of  the  driven  pulley  one  inch  back  of  the  centre  of  the  face  of 
the  driving  pulley,  and  to  give  the  axis  of  the  guide-pulley  an  incli- 
nation of  30°  to  the  horizontal  line. 

The  Shafts  at  Right  Angles  but  not  in  the  same  Plane, 
the  Belt  Running  on  four  Pulleys.    Fig.  45. 

11Y.  Let  E  be  the  driving  shaft, 
with  tight  pulley,  A,  and  loose  pul- 
ley, B,  and  F  the  driven  shaft,  with 
tight  pulley,  D,  and  loose  pulley, 
C  ;  all  the  pulleys  of  same  size  and 
with  rounded  faces,  in  the  usual  way. 

Let  the  pulleys  be  arranged  in  a 
square  on  the  plan,  whose  side  is 
the  diameter  of  pulleys  at  centre 
of  face,  and  let  an  endless  belt  be 
put  on,  as  shown,  and  run  in  the 
direction  of  the  arrow.  It  will  be 
noticed  the  loose  pulleys,  C  and  B, 
run  in  opposite  directions  from  that 
of  the  shafts  on  which  they  turn ; 
but  since  they  carry  the  slack  fold 
of  the  belt,  they  are  relieved  of 
heavy  strain  on  the  shafts.  This 
is  a  good  plan  for  wide  belts  when 
the  shafts  are  a  proper  distance 
apart  —  say  10  times  the  breadth 
of  the  belt  —  and  solves  the  some- 
times difficult  problem  of  carrying 
considerable  power  around  a  corner 
by  a  belt.  There  is  no  loss  of  con- 
tact of  the  belt  on  any  of  the  pul- 
leys of  this  system,  and  no  lateral 
straining  and  tearing  of  the  fibres  of  the  belt,  as  in  the  usual  quarter- 


45. 


176 


METHODS    OF    TRANSMISSION. 


twist  arrangement,  in  which  only  two  pulleys  are  used.  The  lower 
shaft  may  drive  the  upper  one,  as  well,  by  changing  the  direction  of 
motion,  or  changing  the  relative  positions  of  the  tight  and  loose  pulleys. 

The  Shafts  at  Right  Angles  but  not  in  the  same  Plane, 

the  Belt  Running  on  four  Pulleys.     Fig.  46. 

118  •     A  is  the  driving  pulley  on  a  horizontal  main  line-shaft ; 

B  the  driven  pulley  on  a  mill-spindle  or  upright  shaft ;  C  a  tightener 

on  a  shaft  parallel  to  the  main  shaft,  with  bearings,  in  a  frame,  which, 

with  the  pulley,  can  be  raised  or  lowered  when  required  to  start  or 


Fig.  46. 

stop  the  pulley  B ;  D  a  guide  pulley  on  a  vertical  shaft  running  in 
fixed  bearings.  The  course  of  the  belt  is  indicated  by  the  arrows. 
This  plan  may  be  resorted  to  when  the  pulley  A  cannot  be  placed 
on  the  main  shaft  in  a  position  to  receive  the  belt  directly  from  B,  as 
in  the  case  shown  in  Figs.  43  and  44. 

The  Shafts  may  or  may  not  be  at  Right  Angles,  must  be  in  OP 
near  the  same  Plane,  the  Belt  running  on  four  or  five  Pulleys. 
Figs.  47,  48,  and  49. 

119*     Fig.  47  shows  the  usual  method  of  transmitting  power  to 
shafts  which  are  at  or  near  right  angles  with  the  driver,  and  Figs. 


METHODS    OF    TRANSMISSION. 


177 


48  and  49  show  an  extension  of  this  method  to  driving  two  such  shafts 
from  one. 


Fig,  47. 

Let  A  be  the  driving  pulley  on  the  main  shaft,  F  H ;  D  and  E 
driven  pulleys  on  the  counters,  at  right  angles  to  the  main.  Place 
two  upright  shafts,  each  with  a  loose  pulley,  so  that  its  face  will  be 
opposite  the  middle  of  the  face  of  A,  one  to  the  right  and  one  to  the 
left,  over  these  pass  a  belt  as  shown  in  the  cuts.  The  belt  will  run 
either  way  in  both. 

In  Figs.  48  and  49  it  will  be  observed  that  the  driving  face  of  the 
belt  is  changed  between  the  two  pulleys,  D  and  E,  which  may  be 
avoided  by  giving  the  belt  a  half  twist  in  this  part,  which  we  think, 
'  12 


178 


METHODS    OF    TK ANSMISSION. 


however,  would  injure  the  belt  more  than  by  using  both  sides  of  the 


same. 


Collars  O  and  O  are  placed  over  the  pulleys  B  and  C,  and  we  have 
added  the  stationary  flanges  J  and  J  to  the  uprights  under  the  pul- 
leys, introduced  by  Messrs.  Wm.  Sellers  &  Co.,  Philadelphia.  This 
device,  whether  applied  to  vertical  or  horizontal  pulleys,  is  in  every 


Fig.  48. 


Fig.  49. 

way  superior  to  flanges  fast  to  pulleys  which  tend  to  lift  the  edges 
of  the  belts,  and  turn  them  over.  On  the  other  hand,  when  the  belts 
strike  stationary  flanges,  they  are  thrown  back  on  the  pulley  faces 
again,  except,  perhaps,  in  the  case  of  soft,  flabby  belts,  which  are 
liable  to  curl  at  the  edges  and  roll  up. 

The  Shafts  may  be  at  any  Angle  with  each  other,  may  not  be 
in  the  same  Plane,  the  Pulleys  may  differ  much  in  Diameter, 
and  the  Belt  may  be  crossed. 

120.     What   cannot   be   done  with  the  preceding  methods   of 
arranging  the  quarter-twist  belt,  may  be  done  by  the  guide  pulley 


METHODS    OF    TRANSMISSION. 


179 


devices  shown  in  Fig.  50,  in  which  the  vertical  cylindrical  staff,  A, 
is  secured  to  a  flange,  J,  and  held  by  a  brace,  G,  to  an  over-head 
timber,  H,  or  other  fixture. 


Fig,  50. 

Upon  this  staff  are  placed  two  hubs,  F,  held  by  set  screws  in  any 
position,  and  each  formed  with  a  flat  face,  to  which  a  flanged  bracket, 
C,  is  bolted. 

The  upper  bolt,  D,  is  utilized  as  an  axis  about  which  the  bracket 
can  turn,  and  the  lower  bolt,  E,  in  a  slot  permits  the  turning  and 
holds  the  bracket  at  the  inclination  required  by  the  belt. 

In  the  centre  of  each  flange,  C,  is  secured  a  pin,  I,  upon  which  the 
pulleys,  B,  turn. 

The  facility  with  which  these  pulleys  may  have  their  axes  inclined 
to  accommodate  the  angle  of  a  belt  passing  from  a  smaller  to  a  larger 
pulley,  from  a  higher  to  a  lower  shaft,  and  crossing  to  the  opposite 
faces  of  pulleys,  favors  the  employment  of  this  combination,  which 
has  an  all  but  universal  adjustment,  in  many  places  where  the  pre- 
viously described  arrangements  will  not  serve  at  all. 

The  writer,  early  in  February,  1871,  was  required  to  manage  a 
case  of  belting  two  shafts,  set  at  right  angles,  one  above  the  other, 
having  pulleys  of  different  diameters  which  were  to  run  in  opposite 


180  METHODS    OF    TRANSMISSION. 

directions,  and  all  of  them  lying  close  to  one  another.  This  was  dis- 
posed of  successfully  by  the  use  of  mechanism,  exactly  like  that 
shown  in  Fig.  50,  and  this,  with  that  shown  in  Fig.  47,  are  existing 
methods  employed  at  the  People's  Works,  Philadelphia,  for  belt 
driving  around  corners  and  in  confined  places.  * 

Holes  for  Quarter-turn  Belts. 

121.  Draw  on  a  level  floor,  with  chalk  line  and  tram,  two  full- 
size  views  'of  the  pulleys  and  position  of  the  floor  through  which 
belts  are  to  pass,  or  lay  them  down  on  paper  to  a  convenient  scale : 
observing  that,  that  fold  of  the  belt  which  leaves  the  face  of  one  pulley 
must  approach  the  centre  of  the  face  of  the  other  in  a  line  at  right  angles 

to  the  axis  of  the  latter.  Completing 
the  figures  as  shown  in  Fig.  51,  the 
points  of  intersection  a  b  c  and  d  will 
indicate  the  places  in  the  floor,  E  F, 
where  the  centres  of  both  folds  of  the 
belt  will  pass  when  drawn  tightly  and 
at  rest.  The  obliquity  of  the  opening 
can  best  be  obtained  by  trial  of  tape 
line  or  narrow  belt  applied  to  the  pulley 
faces  in  position,  passing  through  small 
trial  holes  in  the  floor.  Allowance  in 
the  hole  should  be  made  for  the  sag  of 
slack  fold  of  belt.  This  is  the  usual  safe  and  practical  shop  method. 

Belt  for  Cooling  Shaft  Journals. 

122»  A  very  ingenious  as  well  as  simple  method  of  cooling  a 
journal,  consists  in  placing  an  endless  belt  of  loose  water-absorbing 
texture  on  the  shaft,  as  near  the  heated  part  as  may  be,  and  allowing 
the  lower  bight  to  run  in  cold  water,  which  may  be  held  in  a  vessel 
at  a  convenient  distance  below  the  shaft. 

Continuous  contact  of  the  liquid  band  carries  away  the  heat  of 
friction  as  it  is  produced,  without  spilling  or  splattering  of  water  on 
and  about  the  machinery,  and  without  contact  of  the  lubricant  in 
the  journal  boxes. 

We  have  seen  this  method  successfully  applied  to  the  shafts  of  the 
rolls  of  calico  printing-presses. 

*  Two  shafts  at  any  angle  with  each  other  may  be  effectively  driven  by  two 
belts,  each  having  less  than  an  J  twist  and  each  running  on  two  pulleys,  by 
placing  a  counter-shaft  above  or  below  and  across  the  main  lines  at  or  near 
equal  angles  to  the  main  line  shafts. 


CHAPTEE    III. 

CEMENTS,  ADHESIVES,  AND  FASTENINGS  FOR  BELTS. 

Cement  fop  Cloth  or  Leather.    Molesworth. 
123  •     16  gutta-percha,  cut  small. 


4  India-rubber, 
2  pitch, 

1  shellac, 

2  linseed  oil, 


melted  together 

and 
well  mixed. 


Water-proof  Cement  for  Cloth  or  Belting.    Chase. 

124.  "  Take  ale,  1  pt. ;  best  Russia  isinglass,  2  oz. ;  put  them 
into  a  common  glue  kettle,  and  boil  until  the  isinglass  is  dissolved ; 
then  add  4  oz.  of  the  best  common  glue,  and  dissolve  it  with  the 
other ;  then  slowly  add  1^  oz.  of  boiled  linseed  oil,  stirring  all  the 
time  while  adding  and  until  well  mixed.  When  cold  it  will  resem- 
ble India-rubber.  When  you  wish  to  use  this,  dissolve  what  you 
need  in  a  suitable  quantity  of  ale  to  have  the  consistence  of  thick 
glue.  If  for  leather,  shave  off  as  if  for  sewing,  apply  the  cement 
with  a  brush  while  hot,  laying  a  weight  on  to  keep  each  joint  firmly 
for  6  to  10  hours,  or  over  night." 

Elastic  Varnish.     Smithsonian  Report. 

125*  "  2  pts.  rosin,  or  dammar-resin,  and  1  pt.  caoutchouc  are 
fused  together,  and  stirred  until  cold.  To  add  to  the  elasticity,  lin- 
seed oil  is  added.  Another  varnish  for  leather  is  made  by  putting 
pieces  of  caoutchouc  in  naphtha  until  softened  into  a  jelly,  adding  it 
to  an  equal  weight  of  heated  linseed  oil,  and  stirred  for  some  time 
together  while  over  the  fire." 

To  Render  Leather  Water-proof.     Mackenzie. 

12S*  "  This  is  done  by  rubbing  or  brushing  into  the  leather  a 
mixture  of  drying  oils,  and  any  of  the  oxides  of  lead,  copper,  or  iron, 
or  by  substituting  any  of  the  gummy  resins  in  the  room  of  the  metal- 
lic oxides." 

181 


182       CEMENTS,    ADHESIVES,    AND    FASTENINGS. 

Water-proof  Glue.     Mackenzie. 

127 •  "Fine  shreds  of  India-rubber  dissolved  in  warm  copal  var- 
nish make  a  water-proof  cement  for  wood  and  leather." 

Another. 

Glue,  12  oz. ;  water  sufficient  to  dissolve  it;  add  3  oz.  of  rosin,  melt 
them  together,  and  add  4  parts  of  turpentine  or  benzine.  Mix  in  a 
carpenter's  glue-pot  to  prevent  burning. 

To  Preserve  Leather  from  Mould.     Mackenzie. 

128.  "  Pyroligneous  acid  may  be  used  with  success  in  preserving 
leather  from  the  attacks  of  mould,  and  is  serviceable  in  recovering  it, 
after  it  has  received  that  species  of  damage,  by  passing  it  over  the 
surface  of  the  hide  or  skin,  first  taking  due  care  to  expunge  the 
mouldy  spots  by  the  application  of  a  dry  cloth." 

Castor-Oil  as  a  Dressing  for  Leather.     Mackenzie. 

129*  "  Castor-oil,  besides  being  an  excellent  dressing  for  leather, 
renders  it  vermin-proof.  It  should  be  mixed,  say  half  and  half,  with 
tallow  or  other  oil.  Neither  rats,  roaches,  nor  other  vermin  will 
attack  leather  so  prepared." 

Adhesive. 

130.  A  good  adhesive  for  leather  belts  is  printer's  ink.     I  have 
the  case  of  a  6-inch  belt  running  dry  and  smooth  and  slipping,  which 
la.tter  was  entirely  prevented  for  a  year  by  one  application  of  the 
above. 

To  Fasten  Leather  to  Metal. 

131.  "A.  M.  Fuchs,  of  Bairere,  says  that  in  order  to  make 
leather  adhere  closely  to  metal,  he  uses  the  following  method :  The 
leather  is  steeped  in  an  infusion  of  gall  nuts ;  a  layer  of  hot  glue  is 
spread  upon  the  metal,  and  the  leather  forcibly  applied  to  it  on  the 
fleshy  side.    It  must  be  suffered  to  dry  under  the  same  pressure.    By 
these  means  the  adhesion  of  the  leather  will  resist  moisture,  and  may 
be  torn  sooner  than  be  separated  from  the  metal." — Athenaeum. 

Dressing  for  Leather  Belts. 

132.  "  One  part  of  beef  kidney  tallow  and  two  parts  of  castor- 
oil,  well  mixed  and  applied  warm. 

"  It  will  be  well  to  moisten  the  belt  before  applying  it.  No  rats 
or  other  vermin  will  touch  a  belt  after  one  application  of  the  oil.  It 


CEMENTS,    ADHESIVES,    AND    FASTENINGS.       183 

makes  the  belt  soft,  and  has  sufficient  gum  in  it  to  give  a  good  adhe- 
sive surface  to  hold  well  without  being  sticky. 

"  A  belt  with  a  given  tension  will  drive  34  per  cent,  more  with  the 
hair  side  to  the  pulley  than  the  flesh  side." —  F.  W.  Bacon,  N.  Y. 

Cement. 

133.  "  A  cement  for  joining  pieces  of  leather,  one  which  repeated 
tests  have  shown  to  be  very  efficient,  may  be  made  by  dissolving  in 
a  mixture  often  parts  of  bisulphide  of  carbon  acd  one  part  of  oil  of 
turpentine,  enough  gutta-percha  to  thicken  the  composition.     The 
leather  must  be  freed  from  grease  by  placing  on  it  a  cloth,  and  press- 
ing the  latter  with  a  hot  iron.     It  is  important   that  the  pieces 
cemented  be  pressed  together  until  the  cement  is  dry." 

Water-proof  Cement  for  Belting.     Moore. 

134.  "Dissolve  gutta-percha   in    bisulphide  of  carbon  to  the 
consistence  of  molasses ;   warm  the  prepared   parts  and  unite  by 
pressure." 

"  To  increase  the  power  of  rubber  belting,  use  red  lead,  French 
yellow,  and  litharge,  equal  parts ;  mix  with  boiled  linseed  oil  and 
japan  sufficient  to  make  it  dry  quick.  This  will  produce  a  highly 
polished  surface." 

Fastenings,  Etc. 

133.  From  various  authorities  we  have  many  ways  of  securing 
and  treating  belts.  "Down  East"  we  find. shoe-pegs  used  for  joining 
the  ends,  which,  being  scarfed,  glued,  and  pressed  together  forcibly, 
have  the  pegs  dipped  in  glue  and  driven  in,  and  when  dry  pared  off 
smoothly.  Such  joints  are  warranted  to  stand  as  long  as  the  belt, 
but  will  not  resist  water  unless  joined  by  water-proof  glue. 

Dried  eel-skin  lacings,  slit  lengthwise  of  the  animal,  are  recom- 
mended for  their  ever  enduring  qualities,  but  these  were  known  long 
ago  on  the  other  side  of  the  Atlantic.  (See  Arts.  39  and  67.) 

A  simple  adhesive  for  rubber  belts  is  made  by  sticking  powdered 
chalk,  which  has  been  evenly  sprinkled  over,  to  the  surface  of  the 
belt  by  cold  tallow  or  boiled  linseed  oil. 

Oil  can  be  taken  out  of  belts  without  injury  to  the  leather  by  sev- 
eral applications  of  4  F.  aqua  ammonia. 

Wilson's  Belt-Hooks. 

136.  We  are  indebted  to  Crane  Bros,  for  description  and  illus- 
tration of  the  above,  which  we  present  in  Fig.  52. 


184       CEMENTS,    ADHESIVES,    AND    FASTENINGS. 

^o.  1.  —  The  teeth  go  through  the  belt  and  clinch.  To  be  used 
only  on  belts  running  at  very  high  speed  over  small  pulleys,  and  in 
making  up  belts,  instead  of  lapping,  glueing,  and  pegging. 

No.  2.  —  Is  the  only  belt-hook  in  the  market  that  can  be  used 
repeatedly  and  successfully  more  than  once.  A  hammer  is  all  that 
is  required  to  secure  them  to  belts.  Lay  the  hook  down  on  some- 
thing solid,  with  the  teeth  up,  and  drive  the  belt  down  tight  to  the  plate. 
None  of  the  belt  is  cut  away  by  punching  holes.  The  strain  comes 
in  fifteen  places  instead  of  three,  as  with  lacings.  Belts  can  be  mended 
in  \  the  time  required  for  any  other  hook  or  lacing.  They  will  last 
longer  than  a  dozen  lacings.  They  are  the  only  good  fastening  for 
rubber  or  paper  belts. 


Fig.  52. 

These  hooks  have  been  thoroughly  tried  for  three  years  in  all 
places  —  in  machine-shops,  cotton,  woollen  and  paper  mills  —  and  all 
who  use  them  admit  that  they  are  the  best  and  cheapest  fastening  in 
use,  taking  into  account  the  durability  of  the  hooks,  wear  and  tear, 
and  time  in  mending  belts. 

Blake's  Patent  Belt-Studs. 

137.  This  approved  device  for  fastening  rubber  and  leather 
belting  was  patented  April,  1860,  and  March,  1861,  and  re-issued 
August,  1868,  shown  in  Figs.  53  and  54.  Messrs.  Greene,  Tweed  & 
Co.,  10  Park  Place,  New  York,  have  the  sole  right  to  make  and  sell 
this  invention,  and  during  the  last  four  years  have  supplied  the  studs 
to  over  10,000  manufacturing  concerns  in  the  United  States. 


CEMENTS,   ADHESIVES,   AND    FASTENINGS.       185 


They  are  recommended  to  be  better  and  cheaper  than  either  lacing 
or  hooks.  When  the  above-mentioned  studs  for  fastening  the  ends 
of  belts  were  tested  on  a  6-inch  4-ply  rubber  belt,  the  following  result 
was  obtained : 

Belt-hooks  tore  out  under  a  strain  of        .         .         800  Ibs. 
Lacing  "  "...       1690   " 

Blake's  studs  held  up  to       "  ...       4600   " 

Where  lacing  or  other  methods  of  fastening  are  used,  requiring 
punched  holes,  which  weaken  the  material  of  the  belt,  the  whole 
strain  transmitted  by  the  belt  must  be  carried  by  a  width  section  of 
the  belt  less  by  the  sum  of  the  diameters  of  the  holes,  which,  in  usual 
practice,  is  about  -J  the  width  of  the  belt ;  whereas,  by  the  use  of 
patent  studs,  no  punched  holes  are  made,  the  material  of  the  belt  is 
not  reduced,  and  nearly  the  whole  section  is  available  for  strain,  the 
stud  being  of  such  a  form  and  inserted  in  such  a  manner  as  to  grip 
nearly  its  entire  width. 

Belts  fastened  by  studs  are 
running  now  nearly  four  years 
without  repair.  The  ends  of 
the  belts  are  kept  close  together, 
and  the  studs  do  not  touch  the 
pulleys. 

When  bolts  have  become  too 
rotten  to  hold  lacings,  they  can  be 

fastened  with  these  studs,  which  will  hold  until  the  belts  are  completely 
worn  out.     For  damp  places  these  studs  make  a  secure  fastening. 

In  fastening  belts  by  these 
studs,  the  slit  in  a  leather  belt 
should  be  a  |  inch,  and  in  a 
rubber  belt  f  inch  from  the 
ends,  and  the  studs  inserted  | 
inch  apart. 

The  cuts  above  give  the  form 
of  the  studs,  the  sizes  made,  and  Fig.  54. 

their  position  in  the  joint. 

The  smallest  size  is  used  for  sewing-machine  belts  and  the  like,  the 
next  size,  say,  for  2-inch  belts,  and  the  largest  for  4  and  5-ply  rubber 
and  double  leather  belts. 

Champion  Belt-Hook. 

138.  Fig.  55  will  convey  a  correct  idea  of  the  manner  of  adjust- 
ing this  hook.  It  will  be  observed  that  the  substantial  double  bear- 


Fig.  53. 


186       CEMENTS,    ADHESIVES,    AND    FASTENINGS. 

ing  of  each  hook  precludes  the  possibility  of  its  "tearing  out." 
Shortening  or  taking  up  slack  in  belts  is  only  the  work  of  a  moment 
when  this  hook'  is  used.  It  is  conceded  that  no  belt  fastening  is 
equal  to  this  for  strength.  It  is  less  expensive  than  the  Blake  stud  or 


Fig.  55. 

than  lace  leather;  and,  although  it  costs  more  than  the  "C"  hook,  it  is 
in  the  end  cheaper,  because  it  retains  its  original  shape  in  the  belt,  and 
the  same  hook  can  be  used  over  and  over  again.  It  can  be  adjusted 
with  greater  ease  and  in  much  less  time  than  any  other  belt  fastening. 


139. 


Machine-riveted  Strapping. 

"  Peter  Mclntosh  &  Sons,  Glasgow,  call  attention  to  their 

machine-riveted    strapping, 

riveted  with  copper  or  iron 
wire.  This  new  joining  is 
highly  recommended,  being 


Fig.  56. 


much  stronger  than  hand-sewn,  and  specially  adapted  for  double 
strapping." 

The  Lincolne  Belt-Fastener. 

140.  "  The  disadvantages,  such  as  insufficient  strength  and  loss 
of  time,  attending  the  usual  modes  of  fastening  belts  by  means  of 
sewing  or  of  leather  laces,  are  well  known.  What  worker  in  a 
mechanical  workshop  has  not  had  to  do  with  the  comparatively 
tedious  operations  of  lacing  a  belt?  Several  mechanical  belt-fast- 
eners are  now  in  use.  One  of  the  newest  and  most  ingenious  forms, 
affording  a  very  strong  and  yet  light  joint  by  very  simple  means,  is 
that  which  we  now  illustrate.  It  is  a  Canadian  invention,  and  we 
understand  that,  though  of  very  recent  introduction,  it  is  making 
rapid  headway  both  in  England  and  abroad.  The  fastener  consists 
of  two  pieces  of  tough  curved  plate  (Figs.  57  and  58),  tinned,  to  pre- 
serve them  from  oxidation.  The  buckle  proper  is  curved  as  shown, 
and  formed  with  a  series  of  teeth  at  each  side,  its  width  transversely 


CEMENTS,    ADHESIVES,    AND    FASTENINGS.       187 


Figs.  57,  58. 


to  the  length  of  the  belt  being  rather  less  than  the  width  of  the  belt 
itself.  The  ends  of  the  belt  are  pierced 
with  an  awl,  or  a  special  tool  for  the 
purpose,  from  the  inside,  in  a  some- 
what slanting  direction,  and  the  points 
of  the  teeth  are  inserted  in  these  holes 
through  the  whole  of  the  belt,  so  as  to 
project  at  the  opposite  side  to  that  at 
which  they  are  inserted.  The  plate- 
cover  or  clasp  proper  is  then  slipped 
over  the  projecting  teeth,  of  course  tying  them  securely  fast,  and 
making  the  complete  buckle.  With  very  wide  belts  several  such 
buckles  are  applied.  Such  a  joint  is  clearly  as  applicable  to  India- 
rubber,  gutta-percha,  or  woollen  belts  as  to  those  of  leather." — The 
Engineer,  Jan.  27,  1870. 

Connecting  the  Ends  of  Belts. 

14:1.  "  Two  or  more  oval  slots,  A  A,  Fig.  59,  are  made  near  one 
end  of  the  belt  to  be  joined,  and  in  the  other  end  of  the  same  belt 
D-shaped  slots,  B  B,  are  made,  the  material  being  cut  through  from 
the  middle  of  the  straight 
side  of  the  D  by  an  inci- 
sion parallel  to  the  length 
of  the  belt,  thus  dividing 
the  end  into  T-shaped 
parts. 

"  The  ends  of  the  belt 
are  scarfed,  so  that  when 
engaged  they  will  lie 
closely  to  the  body  of  the 
belt. 

"  In  connecting  the 
ends  of  the  belt,  the  T- 
shaped  parts  are  twisted  £" 

quarter-way  round  and  passed  through  the  oval  slots  in  the  other  end, 
and  then  straightened  up  again,  thus  locking  the  ends  without  the 
aid  of  laces,  metal  clips,  or  buckles." — Howarth,  Mech.  Mag.,  London, 
XCIV.,  p.  289. 

Directions  for  Lacing  Paper  Belting. 

142.  "  For  narrow  belts  butt  the  two  ends  together,  make  two 
rows  of  holes  in  each  end  (thus  obtaining  a  double  hold),  and  lace 
with  lacing  leather,  as  shown  in  Fig.  60. 


188       CEMENTS,    ADHESIVES,    AND    FASTENINGS. 

"For  wide  belts,  where  extra  strength  is  required,  rivet  pieces 

equal  in  length  to  width 
of  belt  on  back  of  each 
end,  and  make  the  con- 
nection with  lacing,  as 
before.  This  belting 
should,  in  all  cases,  be 
put  on  by  the  use  of 
clamps,  secured  firmly 
to  each  end  of  the  belt, 
and  drawn  together  by 

bolts  running  parallel  with  and  outside  the  edge  of  the  belt,  making 

no  allowance  for  stretch. 

"  Wide  belts,  in  dry  places,  can  best  be  connected  with  Wilson's 

belt  hooks,  riveting  down  the  teeth,  thus  making  a  connection  that 

will  not  wear  out." 

Patent  Belt  Fastenings. 

143.  The  Messrs.  J.  B.  Hoyt  &  Co.,  present  a  patent  belt  fasten- 
ing in  the  form  of  a  double-shanked  rivet  with  a  link  or  elongated 
washer,  having  a  perforation  at  each  end  for  receiving  the  end  of 
each  rivet. 

These  rivets  are  used  for  making  butt  as  well  as  lap  joints  in  belts; 
in  either  case  the  belt  is  punched  as  for  lacing,  with  holes  equidistant 
from  the  joint.  The  perforation,  of  course,  being  of  such  size  and 
distance  asunder  as  to  just  allow  the  double  rivet  to  pass  tightly  in 
when  the  whole  is  secured  by  laying  on  the  link  washer  and  ham- 
mering the  ends  of  the  rivets  into  the  countersunk  holes  of  the  latter, 
care  being  taken  to  imbed  both  head  and  washer  in  the  substance 
of  the  belt,  flush  with  the  surfaces,  in  order  that  they  may  not  wear 
by  contact  with  pulleys. 

They  also  have  the  exclusive  right  to  use  a  patent  "rivet  and 
burr."  This  improvement  consists  of  a  conically  formed  head  to 
the  rivet,  which  gives  greater  strength  of  attachment  thereto.  The 
burr  has  a  form  similar  to  that  of  the  head,  and  has  in  addition  a 
central  hole  countersunk  on  top  for  receiving  the  spread  of  metal  of 
rivet  end  when  hammered  into  it.  This  is  the  best  form  of  rivet  that 
can  be  made,  as  it  gives  the  greatest  strength  and  durability  to  all 
the  parts,  and  is  easily  sunk  into  the  substance  of  the  belt  to  a  level 
with  its  surface. 

They  recommend  for  round  belts  a  grooved  pulley  in  which  the 
section  of  groove  shall  be  neither  triangular  nor  semicircular,  but 
rather  that  of  a  spherical  triangle  or  gothic  arch. 


CEMENTS,    ADHESIVES,    AND    FASTENINGS.       189 


This  form  undoubtedly  gives  greater  belt  contact  than  any  other 
with  a  given  amount  of  tension  on  belt. 

They  also  urge  the  importance  of  covering  pulleys  with  leather, 
"  50  per  cent,  more  work  can  be  done  by  machines  without  belts 
slipping  if  so  covered."  "  The  covering  of  pulleys  with  leather,  in 
many  establishments  where  there  is  a  deficiency  of  power,  would 
produce  such  an  improvement  as  to  astonish,  those  not  acquainted 
with  its  value." 

"  Large  pulleys  and  drums  may  be  covered  by  narrow  strips  of 
leather,  wound  around  spirally,  but  narrow  pulleys  should  be  covered 
by  leather  of  same  width  as  pulley  face." 

"  Our  pulley  covering  is  cut  into  strips  of  required  width  cemented 
and  made  of  even  thickness,  by  a  machine,  then  wound  in  coils  like 
belting." 

Good  Methods  of  Lacing. 

144.  The  usual  way  of  joining  the  ends  of  a  belt  —  that  is,  by 
means  of  the  leather  thong  —  is  the  best  after  all,  because  it  is  the 
most  convenient  ;  the  thong  being  an  article  more  readily  obtained 
and  applied  than  any  other  of  the  numerous  and  ingenious  means 
devised  for  securing  the  ends  of  a  belt. 

In  the  use  of  thongs,  it  is  the  practice  of  some  engineers  to  cross 
them  in  lacing  on  both  sides  of  a  belt  ;  with  others,  to  cross  them  on 
the  outside  only,  laying  the  double  strands  evenly  on  each  other  in 
the  line  of  motion  and  on  the  pulley  side  of  the  belt,  which  experi- 
ence proves  to  be  the  better  way. 

We  present,  in  Fig.  61,  a  plan,  altered  from  the  original,  in  which 
the  two  ends,  a  a,  of  the  thong  are  tied  in 
the  middle  of  the  belt,  as  we  do  not  consider 
any  laced  joint  safe  with  the  tie  at  the  edge. 
It  will  be  observed  that  there  is  no  crossing 
of  the  lace  at  all,  and  that  the  holes  are  in 
two  rows  fore  and  aft,  or  "  staggered,"  as  we 
say,  which  favors  the  strength  of  the  belt. 
This  fastening  may  be  a  little  more  tedious 
to  make,  and  may  require  rather  more  con- 
trivance on  the  part  of  the  party  lacing,  yet 
it  is  one  of  the  best  in  existence. 

The  credit  of  producing  this  excellent  joining  is  due  to  Mr.  Wil- 
liam Annan,  of  Morrison,  111.,  and  of  proposing  to  put  the  tie  in  the 
middle  to  the  Eds.  of  Scientific  Amer.,  in  Jan.,  '66. 


"  ' 


CHAPTER    IV. 

VARIETIES  OF  BELTING. 

Raw-Hide  Belt. 

Mr.  Jno.  Mason,  of  Bulkley,  Barbadoes,  presents  a  novelty 
in  the  way  of  belting  that  he  has  been  using  for  driving  centrifugal 
machines  for  the  past  2  years.  He  says :  "  I  found  leather  belting 
gave  so  much  trouble  and  was  so  expensive  that  I  was  induced  to  try 
a  belt  made  of  raw  cow's  hide,  simply  dried  in  the  sun,  cut  perfectly 
straight,  and  the  joints  carefully  stitched  (square  and  even)  with 
common  saddler's  hemp.  I  find  in  practice  that  a  belt  of  this  descrip- 
tion will  last  longer  than  if  made  of  leather,  besides  being  only  i  the 
cost.  I  am  driving  a  line  of  3-inch  shafting  with  an  8-inch  belt  of 
this  description  with  every  satisfaction.  They  are  now  used  here  for 
driving  Weston's  centrifugals,  as  well  as  those  of  Manlove  and 
Elliott.  I  make  them  2|  inches  broad  for  driving  the  latter." — Engi- 
neering, June  19,  187 Jf. 

Sheet-Iron  Belt. 

146.  Mr.  John  Spiers,  of  Worcester,  Massachusetts,  gives  us  an 
account  of  a  sheet-iron  belt : 

"  A  lathe  used  for  turning  rolling-mill  rolls,  compound  geared,  has 
a  48-inch  pulley  on  it ;  this  is  driven  by  an  18-inch  pulley  on  the 
counter-shaft,  which  makes  120  Kpm,  and  is  8  feet  from  the  48-inch 
pulley,  measured  from  centre  to  centre.  Both  pulleys  of  iron, 
smoothly  turned  on  faces. 

"A  7-inch  double  leather  belt  was  used  on  these  pulleys,  but 
would  slip  when  the  turning-tool  became  dull.  This  belt  was 
replaced  by  one  made  of  Russia  sheet-iron,  same  as  used  for  stove- 
pipes and  parlor-stoves,  and  was  riveted  together  in  the  ordinary 
way ;  it  was  7  inches  wide,  and  was  2  inches  longer  than  the  leather 
belt.  This  extra  length  made  up  for  a  want  of  elasticity  in  the 
iron. 

"  During  one  year's  steady  run  this  iron  belt  could  not  be  slipped, 
even  when  a  heavy  *  cut '  on  a  25-inch  roll  was  taken,  which  broke  a 

190 


VARIETIES    OF    BELTING. 


191 


'  Sanderson '  steel  tool  having  a  section  of  2  x  2J  inches,  a  cutting 
surface  of  2|  inches,  a  feed  of  |  inch  per  revolution,  and  an  overhang 
of  4  inches."' 

Alexander  Brothers'  Improvement  in  Wide  Leather  Belting. 
Patented  June  15,  1875. 

147.  We  respectfully  ask  attention  to  the  following  description 
of  a  patented  improvement  in  the  manufacture  of  wide  leather 
belting  shown  fully  in  Fig.  62 : 


Fig.  62. 

The  term  hide,  used  in  this  description,  means  —  the  skin  of  the 
animal  tanned  whole,  the  back  being  in  the  centre,  lengthwise. 

The  term  side,  means  —  one  of  the  halves  of  the  hide,  made  by  cut- 
ting down  the  middle  of  the  back. 

The  ordinary  method  of  making  wide  two  or  more  ply  belts,  as 
shown  in  cross-section  by  Fig.  2,  is  stripping  pieces  of  the  width 
required  from  the  centres  of  hides,  splicing  the  ends,  and  on  this  one 


192  VARIETIES    OF    BELTING. 

ply  building  up  layer  after  layer,  as  many  as  required,  breaking 
joints  with  each  layer,  lengthwise  of  the  belt ;  the  width  of  each 
layer  being,  of  course,  one  piece.  This  brings  the*  back  centre 
(marked  B.  C.  in  the  cuts),  or  firmest  part  of  the  leather,  imme- 
diately in  the  centre  of  the  belt,  the  edges  being  composed  of 
leather  from  the  side  portions  of  the  hide  (S.  E.)}  which  is  yielding 
in  comparison  with  the  middle.  The  above  construction  has  three 
disadvantages : 

1st.  All  pulleys  being  more  or  less  convex  on  their  faces,  the 
middle  of  the  belt  being  firm  and  not  conforming  to  this  convexity, 
and  the  edges  of  comparatively  loose  fibre,  the  consequence  is  that 
the  edges  of  the  belt  will  not  bind  down  to  the  edges  of  the  pulley, 
and,  after  running  a  short  time,  will  stretch  more,  owing  to  their 
loose  fibre  and  the  absence  of  that  lateral  support  which  the  central 
portions  have..  Thus  only  a  part  of  the  width  of  the  belt  is  effective, 
thereby  transmitting  much  less  power  than  if  all  the  surface  contact 
was  fully  available. 

2d.  The  centre  or  tight  portion  of  the  belt  bearing  the  greater  part 
of  the  strain,  and  the  other  parts  not  relieving  it,  will  consequently 
give  out  proportionately  quicker  than  if  the  strain  was  equalized. 

3d.  Along  the  portion  of  the  hide  over  the  back-bone  full  or 
humpy  places  are  often  found,  caused  by  the  shape  of  the  animal,  and, 
this  part  of  the  leather  being  more  or  less  hard  and  stubborn,  it  is 
difficult  and  often  impossible,  in  the  whole  hide,  to  work  them  perfectly 
flat;  and,  after  being  made  into  belting,  they  present  to  view  an  uneven 
surface  all  along  the  centre  of  the  belt,  which  will  never  lay  down  flat 
to  the  pulley,  thus  preventing  other  parts  from  touching,  and  a  cor- 
responding decrease  in  surface  contact,  even  though  the  edges  were 
supposed  to  bear. 

We  overcome  the  above  disadvantages  by  the  following  construc- 
tion: 

In  making  wide  double  belts  we  cut  the  hides  along  the  middle, 
turn  the  back  edges  (B.  E.)  outward,  and  the  side  edges  (S.  E.) 
inward,  inserting  a  side  centre  <J3.  C.)  piece,  so  as  to  break  joints 
widthwise,  as  shown  m  Fig.  3,  Fig.  1  being  a  perspective  view  of  the 
same. 

In  three-ply  belts  the  same  method  is  carried  out  as  shown  in 
Fig.  4. 

There  are  various  other  arrangements  of  the  pieces  which  can  be 
used  advantageously  in  certain  cases. 

The  disadvantages  of  the  ordinary  method  heretofore  enumerated 
are  overcome  as  follows : 


VARIETIES    OF    BELTING.  193 

1st.  The  edge  portions  of  the  belt  being  of  firm,  solid,  and  un- 
yielding leather,  and  the  middle  portions  of  leather  of  looser  fibre 
and  more  yielding  texture,  it  is  evident  that,  after  running  a  short 
time,  the  middle  will  give  to  the  higher  part  of  the  pulley,  and  the 
edges  will  not  only  bind  down,  but  will  also  afford  that  lateral  sup- 
port which  will  prevent  the  middle  stretching  as  much  as  it  otherwise 
would,  and  thus  giving  an  even  bearing  the  whole  breadth  of  the  belt, 
and  consequently  the  greatest  amount  of  pulley  contact. 

2d.  When  the  middle  of  the  belt  becomes  stretched,  and  allows 
the  edge  portions  to  bed  themselves  down  to  the  pulley,  the  working 
strain  will  be  distributed  over  the  entire  width,  thus  preventing  wear 
on  any  one  part  alone. 

3d.  Cutting  down  the  middle  of  the  hide  enables  the  currier  to 
work  out  any  uneven  or  full  places,  the  surplus  being  cut  away  in 
straightening. 

For  belts  of  16  to  48  inches,  or  wider,  no  other  plan  of  making, 
or  material  other  than  solid  oak  leather,  can  approach,  for  effective- 
ness and  durability,  the  arrangement  described  and  illustrated  above. 

Vulcanized  Rubber  Belts. 

148.  We  are  indebted  to  Mr.  D.  P.  Dieterich,  Esq.,  of  308 
Chestnut  street,  Philadelphia,  agent  for  the  New  York  Belting  and 
Packing  Company,  the  oldest  and  largest  manufacturing  firm  in  the 
United  States  of  vulcanized  rubber  fabrics  adapted  to  mechanical 
purposes,  for  the  following  valuable  collection  of  facts  and  statements 
concerning  rubber  belts : 

"  This  belting  is  made  of  heavy  cotton  duck,  weighing  2  Ibs.  per 
yard,  woven  expressly  for  the  purpose,  and  is  vulcanized  between 
layers  of  a  patent  metallic  alloy,  by  which  process  the  stretch  is 
entirely  taken  out,  the  surface  made  perfectly  smooth,  and  the  sub- 
stance thoroughly  and  evenly  vulcanized. 

"The  superiority  of  this  belting  over  the  best;  leather  belts 
has  been  proved  by  a  trial  of  more  than  10  years.  It  is  manufac- 
tured by  a  process  peculiar  to  this  company,  by  which  unusual 
firmness  and  solidity  are  obtained,  thereby  obviating  some  objections 
heretofore  urged  against  India-rubber  belting  made  in  the  old  way. 

"  This,  together  with  the  fact  that  other  great  improvements  have 
been  made  in  its  quality,  warrants  us  in  asserting  that  it  is  superior 
to  leather,  or  anything  else,  for  all  open  belts,  particularly  heavy  or 
main  belts,  for  the  following  reasons  :  It  has  a  perfectly  smooth  and 
even  surface.  It  seldom,  and  scarcely  ever,  requires  tightening  more 
13 


194  VARIETIES    OF    BELTING. 

than  once.  It  will  always  run  straight  and  with  perfect  bearing  on 
the  pulleys,  by  which  we  believe  that  a  power  of  20  per  cent,  is 
gained  over  the  best  leather  belts.  It  will  stand  heat  of  300°  Fahr. 
without  being  affected,  and  the  severest  cold  will  not  stiffen  it  or 
diminish  its  pliability.  It  is  much  stronger  than  leather  and  far 
more  durable.  It  can  constantly  be  run  in  wet  places  or  exposed  to 
the  weather  without  injury. 

"  From  information  which  we  have  personally  collected  on  the 
subject  of  vulcanized  India-rubber  belting,  it  appears  to  us  that  this 
material  is  yet  designed  to  effect  an  economic  revolution  in  driving 
machinery. 

"  In  the  extensive  establishment  of  Burr  &  Co.,  Cliff  street,  New 
York,  where  the  manufacture  of  hat  bodies  is  carried  on,  and  where 
an  immense  amount  of  belting  is  used,  it  has  taken  the  place  of  leather 
in  nearly  all  work.  We  instance  this  case  because  the  machinery  in 
this  manufactory  is  such  as  to  afford  a  signal  test  of  the  quality  of 
belting.  One  long  India-rubber  belt,  8  ply  and  36  inches  wide,  is 
employed  to  transmit  the  power  from  a  fly-wheel  of  2  horizontal 
steam-engines  of  100  horse-power  each. 

"  The  fan-blowers  of  the  '  forming  machines/  and  those  for  teasing 
and  cleansing  the  fur,  are  driven  at  the  high  velocities  of  from  3000 
to  3500  Kpm.  This  speed  wore  out  the  best  leather  belts  faster  than 
those  of  India-rubber,  which  have  supplanted  them. 

"  India-rubber  belting  has  been  for  some  time  used  for  driving  the 
presses  on  which  the  Scientific  American  is  printed,  and  has  proved 
superior  in  every  respect  to  the  leather  belts  previously  employed. 
It  also  possesses  the  qualities  of  running  unaffected  under  exposure 
to  water,  to  the  open  air,  and  even  to  a  temperature  above  the  boiling 
point. 

"A  5-ply  India-rubber  belt,  12  inches  wide,  as  now  manufactured, 
is  considered  equal  to  a  double  leather  belt  of  the  same  width,  and 
can  be  furnished  at  Jj}$  of  the  price  of  the  latter. 

"The  new  variety  of  India-rubber  belting  to  which  we  have  referred 
is  manufactured  by  the  New  York  Belting  and  Packing  Company  at 
Newtown,  Conn. 

"The  cotton  duck  which  gives  the  peculiar  uniform  and  non-elastic 
character  to  such  material  is  woven  especially  for  this  purpose,  with 
the  warp  much  stronger  than  the  filling,  and  cut  by  machinery  into 
strips  of  a  perfectly  regular  width.  Single  strips  of  this  duck  will 
bear  a  tensile  strain  of  200  Ibs.  to  the  inch  of  width." 


VARIETIES    OF    BELTING. 

Experiments  with  Belting. 

"  The  comparative  adhesion  of  vulcanized  gum  and  leather  belts 
to  the  surfaces  of  pulleys  is  a  question  of  great  interest  to  manufac- 
turers, and  in  order  to  satisfactorily  decide  it,  Mr.  J.  H.  Cheever,  of 
the  New  York  Belting  and  Packing  Co.,  made  a  series  of  experi- 
ments, the  results  of  which  are  here  given : 

"  The  apparatus  consisted  of  3  equal  size  iron  pulleys,  with  faces 
turned  in  the  usual  way  and  secured  to  a  horizontal  shaft,  also  fixed. 
One  of  these  pulleys  was  used  without  covering,  one  was  covered 
with  leather,  and  one  with  vulcanized  gum. 

"  In  the  first  set  of  experiments  a  leather  belt  was  used  of  good 
quality,  3  inches  wide  and  7  feet  long,  with  32  Ibs.  weight  attached 
to  each  end,  and  the  belt  thus  prepared  was  laid  on  the  iron  face 
pulley.  Additional  weights  were  then  attached  to  one  end  of  the 
belt  until  it  began  to  slip,  which  was  in  this  case  found  to  be  48  Ibs. 

"  When  this  weighted  belt  was  placed  on  the  leather-covered  pulley 
it  required  a  weight  of  64  Ibs.  to  slip  it,  and  when  on  the  vulcanized 
gum-covered  pulley  it  required  128  Ibs.  to  slip  it. 

"In  the  second  set  of  experiments,  a  3-ply  vulcanized  gum  belt  of 
the  same  width,  length,  and  thickness  was  used,  and  to  each  end  was 
attached  the  same  weight  as  in  the  other  case. 

"  To  cause  this  belt  to  slip  on  the  iron  face  pulley  required  90  Ibs. 
additional  weight,  on  the  leather-covered  pulley  128  Ibs.,  and  on  the 
vulcanized  gum-covered  pulley  183  Ibs. 

"  In  the  third  set  of  experiments,  the  shaft,  with  all  the  pulleys 
secured  thereto,  was  permitted  to  turn  freely  in  its  bearings.  One 
end  of  the  belt  was  fastened  to  the  frame  work  of  the  apparatus,  and 
to  the  other  end  was  attached  a  weight  of  32  Ibs.  as  before. 

"  A  rope  was  wound  several  times  around  one  of  the  pulleys,  with 
one  end  made  fast  to  the  rim,  and  the  other  allowed  to  hang  freely 
downward ;  to  this  end  weights  were  attached  sufficient  to  produce 
rotation  of  the  shaft. 

"  The  results  were  the  same,  requiring  in  effect  the  same  amount 
of  weight  on  the  end  of  the  rope  to  rotate  the  pulleys  under  the  belt 
as  it  did  on  one  end  of  the  belt  to  slip  the  belt  over  the  pulleys." 

How  to  Use  Vulcanized  Rubber  Machine  Belting. 

"Belts  should  be  cut  T3^-inch  shorter  for  every  foot  of  length 
required.     After  running,  say,  for  3  weeks,  take  up  the  slack  and 
they  will  never  again  require  shortening. 
.  "  To  fasten  the  ends  of  narrow  belts,  make  2  rows  of  holes  in  each, 


196  VARIETIES    OF    BELTING. 

butt  the  ends  together  and  unite  by  strips  of  lacing  leather  in  the 
usual  way  with  leather  belts. 

"  To  secure  the  ends  of  wide  belts,  lap  the  joint  evenly  on  the  out- 
side with  a  piece  of  square  gum  or  leather,  equal  in  width  to  the 
belt,  and  rivet,  sew  or  lace  the  same  firmly  to  each  end  of  the  belt. 

"  If  belts  should  slip  from  dust  or  other  causes,  they  should  be 
slightly  moistened  on  the  pulley  side  with  boiled  linseed-oil,  making 
several  applications  if  necessary.  Animal  oils  must  never  be  used,  and 
belts  should  be  protected,  while  running,  from  contact  with  such  oils. 

"  Should  the  rubber,  from  long  use,  or  other  cause,  be  worn  from 
the  surface  of  the  belt,  give  it  a  coat  or  two  of  lead  paint,  containing 
sufficient  Japan  to  dry  it  quickly. 

"  For  belts  which  are  shifted,  put  rolls  on  the  shifter  bars  with 
axes  inclined  towards  each  other  at  top  and  bottom,  according  to  cir- 
cumstances, which  has  the  effect  to  press  the  faces  of  the  belts  and 
relieve  the  edges  from  wear.  By  this  plan  belts  are  more  easily 
shifted  than  by  the  usual  method,  and  the  liability  to  injure  the 
edges  entirely  prevented.  Use  large  headed  bolts  or  rivets  for  secur- 
ing elevator  buckets." 

General  Statements. 

"  The  more  nearly  horizontal  a  belt  can  be  applied,  the  better  will 
the  weight  of  the  belt  produce  a  sufficient  and  uniform  friction ;  and 
a  long  belt  is  better  than  a  short  one,  inasmuch  as  the  weight  and 
1  sag,'  and  consequently  the  friction,  are  greater. 

"  To  avoid  kinks  and  crooks  in  the  belts,  the  ends  where  joined 
should  be  cut  exactly  square  across  the  centre  line  of  the  belt. 

"  The  pulleys  should  be  perfectly  smooth,  and  the  shafts  carrying 
the  pulleys  perfectly  (in  line,'  parallel  to  each  other,  and  in  the  same 
plane. 

"Leonard,  in  his  'Mechanical  Principia,'  assumes  the  ordinary 
velocity  of  belts  to  be  25  to  30  feet  per  second,  and  gives  a  table 
which  may  be  fully  represented  by  the  following : 


In  which  HP  —  horse-power  transmitted. 
"  w  =  width  of  belt  in  inches. 

"  d  =  diameter  of  smaller  pulley  in  feet. 


VARIETIES    OF    BELTING.  197 

"  Where  belts  are  not  to  be  exposed  to  saturation  of  animal  oil,  or 
to  frequent  abrasion,  a  combination  of  rubber  and  canvas  has  proved 
to  be  fully  equal  if  not  superior  to  leather,  and  is  much  cheaper. 
For  large  belts  rubber  is  preferable,  because  the  belt,  whatever  its 
length  or  width,  is  one  —  not  pieces  joined  by  mechanical  means  or 
connected  temporarily  —  but  solid,  and,  to  all  intents  and  purposes, 
one  continuous  fabric. 

"  For  purposes  where  unusual  strength  is  required  —  equivalent  to 
double  leather  —  5  and  '  6-ply '  belts  are  made.  Endless  belts  of  any 
width  or  length  are  made  to  order,  costing,  in  addition  to  cost  of 
belt,  the  price  of  3  feet  of  the  belt  joined,  for  joining.  For  belts  less 
than  6  inches  wide,  the  3-ply  is  sufficiently  strong,  unless  the  work  is 
unusually  heavy.  Belts  wider  than  6  inches  should  not  be  less  than 
4-ply,  unless  the  work  is  light. 

"Wherever  double  leather  belts  of  14  inches  wide  and  upward 
have  been  used,  we  recommend  our  5  and  6-ply  belts,  and  will  war- 
rant them  to  do  more  work  at  about  one-half  the  cost. 

"  As  an  evidence  of  the  capacity  of  this  establishment,  we  refer  to 
the  '  Champion '  belt,  the  largest  belt  ever  made  of  either  leather  or 
rubber.  It  is  4  feet  wide,  320  feet  long,  and  weighs  3,600  Ibs. 

"  This  company  is  prepared  to  make  any  width  of  belt  not  exceed- 
ing 50  inches. 

"  The  3-ply  vulcanized  gum  belt  weighs  If  Ibs.  to  the  square  foot, 
the  4-ply  weighs  2  Ibs.  Thicknesses  as  follows :  2-ply,  T3g-inch ;  3-ply, 
sVinch  ;  4-ply,  T5rmch  ;  5-ply,  f\-inch ;  6^ply,  ^-mch." 

Edge-laid  Belt. 

149.  "  A  better  plan  of  making  a  broad  belt,  than  the  usual 
American  double  leather  belting  sewn  together,  is  made  with  the 
greatest  ease,  of  any  thickness  or  width,  perfectly  equal  in  texture 
throughout,  and  alike  on  both  sides.  It  is  made  by  cutting  up  the 
hides  into  strips  of  the  width  of  the  intended  thickness  of  the  belt, 
and  setting  them  on  edge.  These  strips  have  holes  punched  through 
them  about  |  of  an  inch  diameter,  and  one  inch  apart.  Nails  made 
of  round  wire,  clinched  up  at  one  end  for  a  head,  and  flattened  at 
the  other,  are  used  for  fastening  the  leather  strips  together. 

"  Each  nail  is  half  the  width  of  the  intended  belt,  and  after  the 
strips  are  all  built  upon  the  nails,  the  ends  of  the  latter  are  turned 
down  and  driven  into  the  leather,  thus  making  a  firm  strap  without 
any  kind  of  cement  or  splicings.  When  the  strap  is  required  to  be 
tightened,  it  is  only  necessary  to  take  it  asunder  at  the  step  lines  of 


198 


VARIETIES    OF    BELTING. 


splice,  cut  off  from  one  end  of  the  strap  at  each  step  what  is  required, 
and  piece  up  again  with  wire  nails  or  laces,  going  entirely  through 
the  strap. 


Fig.  63. 

"  In  Fig.  63,  A  represents  one  of  the  nails  used  in  this  form  of  belt- 
ing, B  B  the  belt  in  perspective,  with  the  part  C  C  cut  half  way  to 
show  the  disposition  of  the  nails,  and  D  D  the  step  lines  of  the 
splice." — E.  Leigh. 

Paper  Belting. 

150.  The  Messrs.  Crane  Bros.,  of  Westfield,  Mass.,  who  manu- 
facture Crane's  Patent  Paper  Belting,  have  kindly  communicated 
the  following  facts  concerning  their  new  fabrics  for  driving  belts : 
— "  Our  belts  are  manufactured  from  pure  linen  stock,  and  can 
be  made  of  any  desired  thickness,  width,  and  length.  We  guar- 
antee equal  driving  power  from  equal  surface,  as  from  leather  or 
gum,  and  we  recommend  them  only  for  straight  and  unshifted  belts, 
making  none  less  than  5  inches  wide.  They  will  not  stretch  nor 
change  shape,  and  being  made  all  in  one  piece,  of  even  thickness, 
will  run  smoothly  and  straight.  We  have  proved  them  equal  in 
durability  with  leather,  and  equal  also  in  strength,  where  they  have 
been  arranged  for  one  to  pull  against  the  other.  They  adhere  to 


VARIETIES    OF    BELTING.  199 

the  pulleys  very  closely,  and  generate  no  electricity  while  running. 
They  are  quite  flexible,  and  do  not  crack  in  passing  over  pulleys 
even  as  small  as  6  inches  in  diameter.  They  are  not  affected  by 
heat  at  ordinary  temperatures,  nor  by  dust  or  oil,  but  will  not  run 
in  water.  Being  very  tough,  they  would  answer  a  good  purpose 
for  elevator  belts,  holding  the  bolts  well  and  running  in  a  direct 
line  without  swinging  from  side  to  side. 

"  Compounds  similar  to  those  used  for  stuffing  leather  belts,  or 
black  lead,  mixed  with  sperm  oil,  are  very  good  to  apply  to  our 
belts,  when  dry  and  slipping. 

"  For  endless  and  for  heavy  belts,  our  belting  material  is  not  to  be 
surpassed,  and  when  fitted  to  the  pulleys  at  the  proper  length,  it 
must  remain  so  until  worn  out.  It  is  40  per  cent,  cheaper  than 
leather,  and  for  all  heavy  and  expensive  belts  must  come  into  gen- 
eral use." 

We  present  some  facts  derived  from  testimonials  furnished  to  the 
makers  of  the  paper  belting. 

One  party  says  the  15-inch  paper  belt  gives  us  entire  satisfaction. 
It  drives  all  our  machinery  with  perfect  ease ;  runs  very  straight, 
without  any  swaying  or  sagging ;  is  not  affected  by  temperature ; 
and  there  are  no  indications  of  electricity,  which  we  consider  a 
great  gain. 

Another  party  has  had  a  15-inch  belt,  70  feet  long,  in  use  during  15 
months ;  the  surface  next  to  pulley  is  hardly  marked,  and  shows  no 
indications  of  wear ;  belt  not  touched  since  first  put  on,  for  repairs 
of  any  kind. 

Another  party  says :  "  We  have  been  using  one  of  your  14-inch 
paper  belts  for  the  last  4  months  to  drive  a  paper  engine,  which 
requires  about  13  horse-power.  It  works  to  our  entire  satisfaction, 
and  gives  us  less  trouble  than  any  other  belt  in  the  mill." 

Another  party  has  in  use  a  paper  belt  12  inches  wide,  50  feet  long, 
and  runs  from  the  fly-wheel  of  a  25  horse-power  engine  to  a  pulley 
on  line-shaft,  driving  machinery  which  nearly  exhausts  the  power  of 
the  engine.  It  gives  equal  satisfaction  with  a  leather  belt  formerly 
used  in  same  place.  A  narrower  and  shorter  belt,  crossed  also,  has 
done  quite  as  well  as  a  leather  belt  under  like  circumstances. 

Another  party  has  thoroughly  tested  the  paper  belt,  and  is  en- 
tirely satisfied  therewith.  The  belts  are  12  inches  wide  ;  one  120  feet 
long,  the  other  92  feet ;  they  do  not  stretch  or  slip. 

Another  party  says :  "  The  paper  belt  continues  to  give  good  sat- 
isfaction. It  has  already  been  at  work  on  our  engine  as  long  as  the 


200  VARIETIES    OF    BELTING. 

majority  of  leather  belts  last  in  the  same  place,  and  as  yet  we  can  see 
no  signs  of  wear.  It  does  not  stretch  nor  slip,  and  running  in  the 
open  air,  as  it  does,  it  saves  us  a  great  deal  of  trouble  which  we  have 
had  heretofore  with  a  leather  belt.  Having  had  a  great  deal  of  ex- 
perience, we  do  not  hesitate  in  saying  that  the  paper  is  a  superior 
belt." 

Water- proofed  Leather  Belting. 

151»  A  company  in  Philadelphia  is  at  present  very  successfully 
engaged  in  water-proofing  various  materials  by  patent  process.  They 
operate  upon  lighter  fabrics  of  all  kinds,  and  also  upon  leather,  and 
claim  to  add  considerably  to  the  durability  and  efficiency  of  belting 
so  prepared.  The  belting  is  rendered  perfectly  water-repellant,  and 
can  therefore  be  employed  under  circumstances  where  the  ordinary 
leather  would  rapidly  stretch  and  become  worthless,  namely,  when- 
ever it  is  exposed  continuously  to  the  wet. 

A  line  of  belting  thus  prepared  has  been  for  some  months  employed 
in  transporting  from  the  bed  to  the  shop  damp  clay,  for  subsequent 
working,  the  clay  being  simply  heaped  upon  the  belt,  and  thus  trav- 
ersed. The  water-proofed  belt  has  thus  far,  we  are  told,  not  appre- 
ciably stretched  or  deteriorated,  which  would  indicate  that  the  pro- 
cess is  a  successful  one,  and  of  much  practical  value. 

The  process,  from  the  account  of  one  who  is  conversant  with  the 
operation,  is  stated  to  be  as  follows : 

"  Leather  bands,  having  the  joints  cemented  and  riveted  in  the 
usual  manner,  are  steeped  in  an  alkaline  solution,  which  permeates 
them  and  forms  a  coating  in  the  surfaces  of  the  cells  and  pores. 

"  By  a  subsequent  treatment  in  a  solution  of  metallic  salts  (some- 
times accelerated  by  pressure),  the  coating  is  rendered  insoluble  and 
repellant  to  water. 

"  The  water-proofing  effect  appears  to  be  thorough,  newly  cut  sur- 
faces being  equally  repellant  to  water  with  the  original.  Belting  so 
treated  possesses  greater  flexibility  and  improved  adhesion  to  the 
pulleys;  about  5  per  cent,  more  force  is  requisite  to  slip  a  band 
after  water-proofing  it  than  before.  In  good  leather,  the  tenacity 
of  fibre  is  not  impaired ;  poor  leather,  or  leather  of  unequal  texture, 
cannot  be  water-proofed  without  so  distorting  it  as  to  render  it  un- 
salable; the  purchasers  of  water-proofed  belts  are  reasonably  sure 
of  good  material. 

"  More  force  is  required  to  stretch  the  belting  after  water-proofing 
than  before,  and  a  considerable  degree  of  elasticity  is  imparted  by  the 
process. 


VARIETIES    OF    BELTING. 


201 


"  The  belting  shortens  or  shrinks  in  length  and  increases  in  width, 
thus  showing  a  tendency  during  the  process  to  resume  the  original 
form  of  the  leather  before  the  stretching  operation  of  the  belt  manu- 
facturer/' 

Underwood's  Patent  Angular  Belting. 

152.  This  driving  belt  consists  of  a  number  of  narrow  leather 
bands,  laid  a- top  of  one  another,  lapping  and  breaking  the  joints,  in 


Fig.  64. 

order  to  secure  the  greatest  combined  strength.     Shown  in  Figs.  64 
and  65. 

To  the  under  side  of  this  compound  band  are  fastened  short  piles 
of  leather,   of   equal    length, 
forming  blocks,  each   secured 
to  the  band  by  two  iron  riv- 
ets, as  shown  above. 

The  4  bands,  J,  are  contin- 
uous ;  the  5  pieces,  K,  and 
shorter  pieces,  I,  interposing, 
are  held  together  by  the  riv- 
ets, F ;  all  are  shaped  to  the 
angle,  C  D  E,  which  is  the 
correct  angle  of  grooves  for 
the  wheels. 

The  length  of  the  blocks  is 
made  as  short  as  construction 
will  permit,  in  order  to  in- 


Fig.  65. 


crease  the  surface  of  contact  while  bending  in  the  groove  of  the 
wheels ;  the  pieces,  I,  are  made  shorter  to  give  more  flexibility  to 
the  baud,  for  which  also  the  blocks  are  separated  by  a  narrow  space. 


202  VARIETIES    OF    BELTING. 

The  elasticity  of  the  leather  is  sufficient  to  allow  of  the  necessary 
bending  of  the  4  united  bands  without  injury  to  the  fibre,  as  it  is  not 
intended  to  use  this  belt  over  pulleys  of  small  diameter. 

The  4  bands,  J,  thus  constituting  the  "  wrapping  connector  "  and 
tensional  strength  of  this  system,  while  the  blocks,  K,  form  the  fric- 
tional  wedges,  so  to  speak,  and  the  sloping  edges  of  all  in  the  angle 
of  the  groove  contribute  to  the  great  adhesive  power  possessed  by 
this  driving  belt. 

The  ends  of  this  belt  are  joined  by  bevelling  the  opposite  faces  of 
the  part  J,  for  18  or  20  inches  of  its  length,  and  then  uniting  the 
whole  by  bolts  having  washers  and  nuts  at  F,  and  with  heads  inside, 
similar  in  size  and  position  to  the  rivets ;  or  the  separated  strands 
may  be  joined,  the  top  one  say  at  O,  the  next  one  at  P,  and  in  no 
case  having  more  than  one  joint  between  any  pair  of  rivets. 

We  have  a  practical  illustration  of  the  driving  capacity  of  this 
kind  of  belt  in  the  N.  H.  and  N.  Y.  Railroad  shops  at  New  Haven, 
Conn.,  where  a  22-inch  double  leather  belt  of  Hoyt's  make,  weighing 
2^  Ibs.  per  square  foot,  running  on  pulleys  of  6  feet  and  4  feet  diam- 
eter, and  16^  feet  distant  between  centres  of  pulleys,  with  a  quarter- 
twist,  and  slipping  under  a  load  of  75  to  80  horse-power,  with  noise 
which  could  be  heard  1|  miles  away,  was  replaced  by  2J-inch  angular 
belts,  on  V-grooved  wheels  of  same  diameter.  After  16  months  of 
running,  one  of  the  angle  belts  was  removed.  This,  of  course,  put 
all  the  work  on  the  remaining  one,  and  this  one  carried  the  whole 
load  with  apparent  ease.  Afterwards  one-third  more  work  was  done 
by  this  belt  without  slipping,  visible  straining,  or  injury. 

20  inches  length  of  the  2^-inch  belt  weighs  2  Ibs.  21  inches  of  the 
3-inch  belt  weighs  3  Ibs.  M  N  is  the  breadth. 

European  Compound  Leather  Belts. 

153*  An  examination  of  the  different  leather  departments,  and 
the  varieties  of  belting  in  actual  use,  reveals  a  tendency  on  the  part 
of  manufacturers  to  improve  the  quality  of  wide  belts  by  securing  2 
inch  strips  along  their  edges.  Specimens  of  this  character  are  ex- 
hibited by  Messrs.  Webb  &  Son,  Stowmarket,  England ;  Mr.  Wil- 
liam Ruland,  of  Bonn,  Prussia;  H.  Lemaistre  &  Co.,  Brussels, 
Belgium;  Placide  Peltereau,  32  Rue  d'Hauteville,  Paris;  Poul- 
lain  Brothers,  99  Rue  de  Flandre,  Paris ;  and  others  of  less  note. 

The  material  forming  these  strips  is  (with  a  single  exception) 
leather  of  the  same  quality  as  the  belt.  The  methods  of  attach- 
ment are  variable,  as  laces,  threads,  rivets,  eyelets,  and  brass  screws. 


VARIETIES    OF    BELTING.  203 

The  English  use  the  threads,  Prussians  the  laces,  and  the  French  all 
the  varieties  enumerated.  Mr.  P.  Pelterau,  proprietor  of  one  of  the 
largest  houses  in  France,  makes  a  remarkable  display,  not  only  of 
belts  and  their  mountings,  but  of  different  kinds  of  leather,  such  as 
tanned  elephant  hide,  varying  in  thickness  from  |  to  \  an  inch,  and 
hippopotamus  hide  from  1  inch  to  1|  inches  in  thickness. 

His  8-inch  and  10-inch  belts  have  leather  facings  2  inches  wide  on 
their  edges.  Each  of  these  facings  is  attached  by  two  leather  laces, 
whose  stitches  have  |  of  an  inch  span,  and  run  in  parallel  lines  sep- 
arated by  1|  inches. 

The  "  inextensible  belt,"  for  which,  at  a  previous  exposition,  he 
received  a  gold  medal,  has  steel  instead  of  leather  edging  strips. 
These  strips,  for  a  10-inch  belt,  are  2  inches  wide  by  g\  of  an  inch 
in  thickness,  and  are  attached  by  2  riveted  rows  of  copper  tacks. 
These  tacks  are  £  inch  diameter  and  placed  3£  inches  between 
centres. 

Messrs.  Poullain  Brothers  join  their  single  and  compound  their 
double  belts  with  headless  ^-inch  brass  screws.  This  is  accomplished 
by  a  very  ingenious  machine,  of  which  there  are  several  types  in 
the  French  department.  It  carries  a  coil  of  plain  brass  wire,  which, 
while  being  fed  to  the  work,  passes  through  a  die  of  28  threads  to 
the  inch.  The  screw  thus  formed  enters  the  belt  at  a  point  closely 
clamped  by  a  foot-lever,  and,  having  passed  through,  is  cut  off. 
Finally,  the  belt  being  placed  on  a  surface-plate,  the  points  of  all 
the  screws  are  slightly  riveted.  The  most  compact  and  expeditious 
of  these  machines  is  the  invention  of  Mr.  Cabourg,  74  Rue  St. 
Honore,  Paris. 

Mr.  E.  Scellos,  of  74  Boulevard  du  Prince  Eugene,  exhibits  what 
he  terms  a  "  homogeneous  belt,"  for  150  horse-power.  This  belt  is 
19J  inches  wide  by  f  inch  in  thickness. 

It  is  composed  of  104  leather  strips  f  inch  wide,  laid  horizontally 
with  reference  to  the  belt,  and  laced  transversely;  the  distance 
between  laces  is  \\  inches,  and  diameter  of  lace  T3g  of  an  inch.  The 
advantage  of  edge-bound  wide  belts,  where  frequent  slipping  is  an 
essential,  we  think  will  be  readily  conceded ;  and  to  what  extent  they 
can  supplant  double  belts  is  a  subject  worthy  of  experimental  inquiry. 
The  use  of  very  wide  belts  is  seldom  resorted  to  in  the  machinery 
department.  One  of  the  stationaries  has  two  central-ribbed  pulley- 
rims  bolted  to  the  arms  of  its  fly-wheel,  on  these  run  4  belts  6  inches 
in  width ;  another  has  two  12-inch  edged  belts,  and  so  on.  The  in- 
clination was  always  to  increase  the  number  rather  than  the  width 
of  the  belts. —  Paris  Exposition,  1867. —  W.  S.  Auchincloss. 


204  VARIETIES    OF    BELTING. 

English  Belts  of  Leather  and  Iron  Mixed. 

154:*  "  A  contemporary  says  that  the  improved  steel  wire  has  a 
strength  of  160  to  175  tons  per  square  inch  of  actual  section ;  that 
176  No.  14  wires  have  a  total  section  of  one  square  inch,  and  that 
each  wire  will  bear  from  2000  Ibs.  to  one  ton  breaking  strain ;  and  that 
the  ropes  made  from  these  wires  run  readily  around  4-feet  or  5-feet 
drums,  coil  perfectly,  and  last  for  a  long  time.  Such  being  the  case, 
it  becomes  important  to  us  to  look  to  steel,  in  a  measure,  to  substitute 
leather  driving-belts."  .  .  . 

"  While  the  substitution  of  leather  by  other  substances,  such  as  the 
vegetable  gums,  gutta-percha,  and  India-rubber,  impregnated  into 
strips  of  coarse  woven  fabrics,  has  often  been  tried,  and  used,  too, 
with  a  certain  measure  of  success.  Speaking,  as  we  now  do,  from  an 
experiment  as  to  the  value  of  such  a  combination  for  driving-belts, 
we  can  certainly  assert  that  we  never  found  them  one-quarter  as 
durable  as  leather ;  their  use  was  more  costly  than  the  older  used 
substance." 

.  .  .  "  In  some,  though  few,  cases  iron  and  steel  wire  belts  have 
been  used,  the  pulleys  on  which  they  run  being  covered  with  buckskin 
or  some  other  leather,  to  increase  the  adhesion." 

"  We  have  cited  these  few  remarks  to  throw  out  the  hint  that,  now, 
when  cheap  and  strong  steel  wire  can  be  purchased,  there  promises 
to  be  a  fruitful  field  for  inventive  talent  to  devise  some  means  of  so 
weaving  steel  wire  and  gutta-percha  into  flat  belting  —  producing  a 
stronger  and  better  adhering  driving  band  than  leather  ever  can  be." 
—Prac.  Mech.  Jour.,  Nov.,  1867,  p.  237. 

Chas.  Sanderson,  of  Sheffield,  England,  has  taken  out  a  patent  — 
dated  Dec.  8, 1862 — "  For  making  driving  bands  of  thin  sheet  metal, 
coated  with  rubber,  to  prevent  oxidation."  "  The  bands  are  first  well 
cleaned  with  acids,  then  coated,  by  electro  process,  with  brass,  after 
which  they  are  coated  all  over  with  gum  vulcanized  thereon,  and 
which  adheres  tenaciously  to  the  metal  coating.  Bands  of  great 
strength  may  be  made  by  cementing  together  several  made  as  above, 
with  a  layer  of  gum  between  each,  the  gum  imparting  flexibility  and 
adhesion  to  the  compound  band  in  passing  over  the  pulleys." 

George  and  Daniel  Spill,  of  Middlesex,  England  —  under  date  of 
Nov.  9,  1859  —  have  taken  out  a  patent  for  "  the  manufacture  of 
bands  by  weaving  together  covered  strips  of  metal  with  ends  of  hemp 
or  other  fibrous  material." 

A  strip,  or  band,  or  wire  of  steel  is  covered  with  one  or  more 


VARIETIES    OF    BELTING.  205 

strands  of  hemp  cord,  previously  passed  through  a  solution  of  caout- 
chouc, gutta-percha,  glue,  drying  oils,  gums,  resins,  tar,  pitch,  or 
other  glutinous,  gelatinous,  or  siccative  materials.  After  the  strands 
have  been  applied,  the  strip  or  wire  is  passed  between  rollers,  in  order 
to  solidify  the  covering. 

Any  required  number  of  metal  strips  or  wires  thus  covered  are 
used  as  warps  in  a  loom,  and  hemp  cord  or  other  fibrous  material  — 
previously  covered  with  a  solution  of  caoutchouc  or  any  of  the  other 
before-mentioned  materials,  or  not  —  is  employed  to  weave  the  whole 
together. 

The  fabric  thus  produced  is  passed  between  rollers,  to  render  it  flat 
and  smooth,  and  before  or  after  so  doing  a  solution  of  caoutchouc, 
gutta-percha,  or  a  coat  of  paint,  or  any  other  desired  material,  is 
applied  thereto. 

M.  J.  Haines,  of  Stroud,  England,  has  taken  out  a  patent  —  bear- 
ing date  Feb.  14,  1860  —  for  making  driving-belts. 

"  This  invention  consists  in  cutting  leather  or  hides  into  narrow 
strips  of  equal  width,  each  strip  width  representing  the  thickness  of 
the  intended  driving-belt,  and  placing  the  same  side  by  side,  break- 
ing joints  with  the  lengths,  to  make  the  whole  of  uniform  strength, 
and  with  the  cut  edges  of  the  leather  coming  to  the  upper  and  under 
surfaces  of  the  intended  belt,  until  the  desired  width  is  obtained. 
The  whole  are  fastened  together  by  wire,  rivets,  or  screws  passing 
transversely  through  the  strips,  and  secured  on  the  opposite  sides." 

"  An  interesting  description  of  American  belting  is  made  chiefly 
of  wool,  and  the  surface  of  the  belt  covered  with  a  resinous  cement. 
We  saw  a  small  piece  that  had  been  in  use  for  2^  years  on  a  heavy 
cloth  loom  in  the  States."— Lond.  Meek.  Mag.,  Mar.,  1863. 

For  description  of  a  peculiar  form  of  driving-belt,  the  invention 
of  W.  Clissold,  see  Frank.  Inst.  Jour.,  Aug.,  1863,  p.  121.  It  consists 
of  double  links  of  leather,  or  other  similar  material,  connected  by 
intermediate  links  of  metal,  the  whole  series  running  in  grooved 
pulleys,  the  leather  only  touching  the  sides  of  the  grooves,  and  driv- 
ing by  adhesion,  in  the  same  manner  as  ordinary  round  belts. 

J.  B.  Hoyt  &  Co.'s  Patent  Angular  Belting. 

155»  "  This  invention  consists  of  a  novel  belt  of  a  trapezoidal 
form,  to  be  used,  in  connection  with  a  V-shaped  or  angular  grooved 
pulley,  for  driving  all  kinds  of  machinery  where  belting  is  required 
to  transmit  power. 

"  The  angular  belt  is  a  great  improvement  on  the  round,  square, 


206  VARIETIES    OF    BELTING. 

or  flat  belt ;  a  much  greater  surface  of  the  belt  is  brought  in  contact 
with  the  pulley  than  with  any  other  kind.  It  will  wedge  itself  into 
the  groove  and  resist  any  slipping  action  during  the  rotation  of  the 
pulley,  so  that  the  greater  the  strain  put  on  one  side  of  the  belt  the 
tighter  will  it  be  held  in  the  groove ;  not  being  liable  to  slip  on  the 
pulley,  it  may  be  used  very  loose,  causing  less  friction,  consequently 
requiring  less  power  to  drive  machinery,  and  giving  it  greater  cer- 
tainty and  regularity  of  motion.  As  the  angular  band  is  not  liable 
to  slip,  it  can  be  used  with  greater  economy  and  certainty  than  either 
the  round  or  flat  belting ;  its  power  is  limited  only  by  its  strength. 
Made  of  the  same  materials  and  the  same  width  of  belt,  this  form 
has  more  strength  than  any  other. 

"  This  belt  has  been  used  with  perfect  success  when  other  bands 
have  failed  entirely  to  impart  motion  to  machinery.  They  are  made 
without  a  joint  in  their  length ;  and  when  the  width  requires  more 
than  one  thickness  of  leather,  the  belt  is  connected,  then  riveted  or 
screwed,  so  that  the  fastening  will  not  come  in  contact  with  the  pulley." 

Friction  Wheels. 

156*  "  Wheels  acting  upon  each  other  are  the  instruments  by 
which  the  transmission  offeree  from  one  part  of  a  system  of  machinery 
to  another  is  commonly  and  conveniently  effected.  The  due  connec- 
tion of  the  moving  parts  is  accomplished  either  by  the  mutual  action 
of  properly  formed  teeth,  by  straps  or  endless  bands,  or  by  the  fric- 
tion of  one  face  of  a  wheel  against  another.  The  latter  method  has, 
when  adopted,  been  generally  in  small,  light  works,  where  the  pres- 
sure upon  the  different  parts  of  the  machinery  is  never  considerable. 
Mr.  Nicholson  saw  a  drawing  of  a  spinning-wheel  for  children,  at  a 
charity  school,  in  which  a  large  horizontal  wheel,  with  a  slip  of  buff 
leather  glued  on  its  upper  surface  near  the  outer  edge,  drove  12  spin- 
dles, at  which  the  same  number  of  children  sat.  The  spindles  had 
each  a  small  roller,  likewise  faced  with  leather,  and  were  capable,  by 
an  easy  and  instantaneous  motion,  of  being  thrown  into  contact  with 
the  large  wheel  at  pleasure.  The  winding  bobbins  for  yarns  at  the 
cotton-mills  operate  on  the  same  simple  and  elegant  principle,  which 
possesses  the  advantage  of  drawing  the  thread  with  an  equal  velocity, 
whatever  may  be  the  quantity  on  the  bobbin,  and  cannot  break  it. 

"We  are  not  aware  that  the  same  mode  of  communication  has 
been  adopted  in  large  works,  except  in  a  saw-mill,  by  Mr.  Taylor, 
of  Southampton.  In  this  the  wheels  act  upon  each  other  by  the 
contact  of  the  end  grain  of  wood  instead  of  cogs.  The  whole  makes 


VARIETIES    OF    BELTING.  207 

very  little  noise  and  wears  very  well ;  it  has  now  been  in  use  nearly 
20  years.  There  is,  of  consequence,  a  contrivance  to  make  the  wheels 
bear  firmly  against  each  other,  by  wedges  at  the  sockets  or  by  levers. 
This  principle  and  method  of  transmitting  power  certainly  deserves 
every  attention,  particularly  as  the  customary  mode,  by  means  of 
teeth,  requires  much  skill  and  care  in  the  execution,  and,  after  all, 
wants  frequent  repairs." — Treatise  on  Mechanics.  Olinthus  Gregory, 
London,  1806. 

English  Leather  Belts. 

1 5V.  Mr.  W.  T.  Edwards,  of  No.  20  Market  Place,  Manchester, 
England,  presents,  October  24,  1875,  the  following  interesting  par- 
ticulars of  English  leather  and  belts:  "All  our  belts  are  made  from 
the  best  English  leather  —  that  is,  English  hides,  oak-bark,  tanned; 
and  to  make  them  any  length  and  width  without  cross  joints,  we 
select  all  the  large  hides  (which  are  curried  on  the  premises) ;  we 
then  cut  the  hide  round  (taking  off  the  bellies  and  shoulders) ;  they 
are  then  cut  spirally  in  narrow  strips,  1J  inches  wide  or  more,  sewn 
together  longitudinally,  in  the  same  manner  as  the  stitching  of  a 
cricket-ball  cover.  Some  of  the  strips  are  160  feet  long.  By  this 
patent  (Sampson's)  we  build  the  belt  any  width ;  the  double  belts 
are  made  by  putting  two  singles  back  to  back,  and  then  pegging 
them  together;  by  these  means  we  get  the  greatest  amount  of  strength 
with  the  least  possible  weight,  an  even  thickness  throughout,  and 
warranted  to  run  perfectly  straight. 

"I  have  just  supplied  a  38-inch  wide  double,  90  feet  long,  for  driv- 
ing direct  from  the  fly-wheel,  14  feet  diameter,  to  a  6-feet  pulley. 
Speed  of  belt,  2800  Fpm,  transmitting  350  horse-power  indicated, 
the  belt  running  horizontally,  and  driving  the  whole  of  the  ma- 
chinery in  a  cotton-mill.  At  another  cotton-mill  I  have  two  29-inch 
wide  double  (121  feet  and  145  feet  long),  driving  pulley  28  feet 
diameter,  5  feet  face  turned  up  for  the  two  belts ;  driven  pulleys,  7 
feet  6  inches  diameter;  speed  of  belts,  4500  Fpm,  running  at  an  angle 
of  75°,  and  transmitting  600  indicated  horse-power. 

"  I  have  in  another  similar  cotton-mill  double  belts  28  inches  wide. 
I  have  a  36-inch  wide  double  turning  about  30,000  throstle  spindles 
in  one  room,  transmitting  350  horse-power  indicated  ;  pulleys  16  and 
8  feet  diameter;  speed  of  belt,  4300  Fpm,  running  at  an  angle  of  45°. 
At  another  spinning-mill  I  have  8  double  and  treble  belts  transmit- 
ting 2000  horse-power  indicated ;  pulleys  10  and  7  feet  diameter ; 
speed  of  belts,  4200  Fpm  on  second  motion  shaft.  I  am  now  making 
two  26-inch  treble  belts,  which  are  intended  to  transmit  800  indicated 


208 


VARIETIES    OF    BELTING. 


horse-power.  I  have  a  24-inch  double  at  Sir  Joseph  Whitworth  & 
Sons'  works  here  transmitting  290  horse-power  indicated ;  pulleys 
each  10  feet  diameter ;  speed  of  belt,  4200  Fpm,  running  horizon- 
tally. I  have  another  24-inch  double  transmitting  230  horse-power 
indicated ;  pulleys  19  feet  6  inches  and  6  feet,  running  horizontally 
at  a  speed  of  2700  Fpm.  I  have  them  up  to  26-inch  wide  trebles 
working  in  rolling-mills  here  in  England.  I  had  a  30-inch  double 
turning  350  horse-power  indicated,  but  they  have  been  induced  to 
put  in  a  wider  belt.  I  have  one  on  hand  now  34  inches  wide.  I 
have  plenty  of  large  belts  working  in  this  country,  and  am  only  giv- 
ing you  a  few  of  the  principal  ones.  To  do  the  same  amount  of  work, 
I  generally  allow  a,  third  more  width  for  single  than  for  double  belts." 

Various  Driving  Belts. 

158*  "The  North  British  Rubber  Company,  Edinburgh,  ex- 
hibited India-rubber  belting  in  various  widths.  This  belting  consists 
of  a  number  of  plies  of  cotton  fabric  cemented  together  by  India- 
rubber,  and  is  said  to  possess  the  advantages  of  durability  and  supe- 
rior adhesion  as  compared  with  leather. 

"  The  machinery  in  motion  in  the  Western  Annex  was  driven  by 
India-rubber  belts  supplied  by  the  exhibitors,  which  worked  in  a 
satisfactory  manner. 

"Messrs.  G.  Spill  &  Co.,  London,  exhibited  machinery  belting 
manufactured  from  flax-yarn,  saturated  with  a  compound  substance, 
said  to  be  incapable  of  decomposition. 

"  The  following  results  of  the  tests  to  prove  the  tensile  strength  of 
this  belting  in  the  chain-cable  testing  machine  at  Rotherhithe  appear 
to  show  that  it  is  much  stronger  than  leather  belting : 


BELTING. 

WIDTH  IN 
INCHES. 

TENSILE  STRENGTH 
IN  LBS. 

TENSILE  STRENGTH  PER 
INCH  WIDE  IN  LBS. 

1 

5 

6272 

1254 

2 

5 

7448 

1489 

3 

10 

16632 

1663 

Stout  leather  band 
of  good  quality.... 

}< 

2100 

'  525 

"Messrs.  Nobes  &  Hunter,  London,  exhibited  compound  leather 
belts,  manufactured  of  a  strong  hempen  web,  sewed  between  2  plies 
of  leather. 


VARIETIES    OF    BELTING. 


209 


"Messrs.  Bryant  &  Cogan,  Bristol,  exhibited  edge-laid  leather  bands, 
consisting  of  thin  strips  of  leather  laid  side  by  side,  breaking  joint, 
and  united  into  one  band  of  the  requisite  width.  It  is  considered 
that  by  the  mode  of  working  the  strap  on  the  edge  of  the  leather 
instead  of  on  the  face,  the  risk  of  cracking  and  breaking  the  grain 
of  the  material  is  avoided ;  whilst  edge-laid  bands  may  be  used  more 
slackly  than  ordinary  bauds,  as  the  edge  surface  '  hugs '  the  drum  or 
pulley  more  than  the  face.  (See  Arts.  149  and  153.) 

"Messrs.  C.  J.  Edwards  &  Son,  London,  exhibited  untanned  leather 
belts.  The  fibres  of  tanned  leather,  he  contends,  are  weakened  by  the 
ordinary  artificial  means  used  in  swelling  the  hides,  which  produce 
heavier  and  thicker,  but  spongy  leather.  Mr.  Preller's  leather  is 
twice  stretched,  and  is  of  greater  density,  as  it  contracts,  in  drying, 
to  the  original  thickness  of  the  hide,  and  from  the  results  of  experi- 
ments made  at  Woolwich  Dockyard,  to  which  he  refers,  it  is  said  to 
have  been  ascertained  that  his  leather  is  at  least  50  per  cent,  stronger 
than  tanned  leather. 

"Mr.  W.  Potier, London, 
exhibited  gut  wheel  bands, 
also  bauds  of  twisted  leath- 
er."— "Exhibited  Machinery 
of  1862."  D.  K.Clark,  C. 
E.,  London. 


Tool  for  Putting  on  Belts. 

loO»  We  copy  from 
an  advertisement  in  "  En- 
gineering" a  very  inge- 
nious device  for  putting 
on  belts  while  the  pulleys 
are  in  motion,  shown  in 
Fig.  66. 

The  conical  pin  and 
flange,  A,  revolve  on  the 
end  of  the  ^taff,  B,  which, 
being  provided  with  a  sock- 
et, may  have  a  rod,  C,  of 
any  suitable  length  fitted 
to  it. 

The  illustration  shows  how  it  is  to  be  used. 
14 


66. 


CHAPTER    V. 

ON  THE  STRENGTH  OF  BELTING  LEATHER. 

160»  "  We  herewith  call  the  attention  of  those  who  use  belting 
to  the  results  of  some  tests  made  for  us  by  Richie's  testing  machine,  as 
to  the  relative  strength  of  different  portions  of  a  side  of  leather  when 
submitted  to  a  breaking  strain.  The  experiment  was  made  with  half 
of  one  of  our  regular  butts,  from  which  48  pieces  were  cut,  each  11| 
inches  long  by  2  inches  wide,  on  which  they  are  respectively  marked, 
with  the  breaking  strain  (in  Ibs.),  stretch  (in  fractions  of  an  inch), 
and  weight  of  each  sample  (in  ounces  and  drams)." 

"  It  will  be  seen  in  table  (Fig.  67)  that  the  textile  strength  of  leather 
varies  widely,  according  to  the  portion  of  the  hide  from  which  the 
leather  is  taken,  and  the  test  shows  that  the  most  valuable  leather, 
or  that  which  insures  an  enduring,  straight,  and  well  running  belt  is 
not  found  in  that  part  of  the  side  which  has  the  greatest  textile 
strength.  The  long  fibre  found  near  the  lower  edge  of  a  side  of 
leather  or  in  a  hide  that  is  not  well  filled  (and  still  stronger  in  a  raw 
hide),  will  stand  a  much  greater  breaking  strain,  but  it  does  not  pos- 
sess those  qualifications  required  for  belting  and  sole  leather  purposes, 
which  are  found  in  the  firmest  part  of  well-filled  oak- tanned  leather." 
—  J.*B.  Hoyt&  Co. 

"  This  test  is  of  importance  principally  to  makers  of  belt  or  band 
leather,  but  when  we  compare  the  results,  and  notice  how  great  is  the 
variation  of  tensile  strength  —  those  parts  which  are  concededly  the 
best  for  sole  leather,  giving  such  decidedly  inferior  qualities  for  belts 
or  for  harness  —  it  is  quite  possible  that  the  experiment  may  have  as 
much  of  value  to  the  makers  of  boots  and  shoes,  as  it  has  to  the 
manufacturers  of  belting ;  for,  generally  speaking,  those  portions  of 
the  hide  which  give  the  greatest  tensile  strength  will  most  readily 
soak  water,  and  present  the  least  resistance  to  wear  by  attrition,  when 
used  in  the  soles  of  boots  and  shoes.  The  leather  which  is  most  care- 
fully made  from  the  best  selected  hides,  and  in  which  the  tanning  is 
most  thorough,  and  nothing  neglected  in  the  finish  and  trim,  will 
undoubtedly  continue,  as  heretofore,  at  all  times  to  command  the 
highest  prices  and  the  readiest  sale." — Shoe  and  Leather  Reporter, 
July  6,  1876. 

210 


STRENGTH    OF    BELTING    LEATHER.  211 

I  have  endeavored  to  present  in  this  chapter  as  complete  an  exhibit 
of  the  tensile  resistance  of  the  beltings  in  general  use  for  machine 
driving  as  could  be  obtained  from  standard  books :  these  were  found 
having  little  to  offer  in  variety,  and  less  to  give  in  the  way  of  details 
of  tests,  but  the  isolated  figures  derived  from  these  sources,  when 
taken  in  connection  with  the  interesting  and  valuable  experiments 
of  the  Messrs.  Hoyt,  together  with  those  made  at  the  Centennial, 
make  up  a  tabular  statement  which  will  enable  the  reader  to  know 
about  what  strength  there  is  in  leather  and  in  some  other  beltings. 

A  glance  at  either  table  will  show  the  user  of  belts  that,  if  he 
employs  such  as  are  well  made  from  good  stock,  he  has  little  to  fear 
from  the  breaking  of  them  in  the  solid  part,  even  when  severely 
used.  To  prove  this,  refer  to  the  articles  in  which  the  driving 
tension  for  continuous  service  is  stated.  Take  Morin's  figures,  for 
example,  in  Art.  1,  p.  17,  indicating  355  Ibs.  to  the  square  inch  of 
leather,  being  equal  to  from  ^  to  T1^  the  breaking  strength  of  the 
same,  which  is  ample  factor  of  safety  even  when  the  belt  has  lost 
part  of  its  original  tenacity  by  wear  and  tear,  and  by  the  weak- 
ening effect  of  oils  and  adhesives  applied  to  its  substance. 

Again,  take  the  strain  of  100  Ibs.  to  the  inch  of  width,  as  proposed 
by  Thurston,  in  Art.  40,  which  is  beyond  the  limits  of  usual  practice; 
but  single  leather  belting  has  been  submitted  to  such  a  working  load 
without  appreciable  injury,  as  represented  in  Art.  15.  Even  this  is 
only  -J-  the  rupturing  strain  of  the  poorest  leathers  in  the  table. 

Account  should  be  taken,  in  these  estimates,  of  the  loss  at  the  holes 
for  rivets  and  laces,  for  the  tightening  to  gain  adhesion,  and  for  the 
weakening  of  the  belt  at  the  splices  and  fastenings,  which  are  favored, 
of  course,  by  the  superior  tenacity  of  the  fibre  of  the  belt. 

Hoyt's  tests  of  a  side  of  leather  have  awakened  an  increasing  inter- 
est in  the  need  of  reliable  experiments  for  determining  the  breaking 
strain  of  the  various  beltings  in  use.  This  table  tells  us  plainly  that 
strength,  stretch,  and  show  of  leather  are  not  equal  and  convertible 
terms,  and  shakes  our  faith  in  the  ancient  saying  that  there  is 
"nothing  like  leather,"  by  proving  it  to  be  not  all  strong,  but,  like 
everything  else,  having  its  weak  points.  It  shows,  also,  why  belts 
become  crooked  in  use. 

The  table  on  page  213  shows  the  strength  of  various  beltings  —  the 
first  group  presenting  the  tests  made  on  July  3,  1876,  at  the  Centen- 
nial Exhibition,  in  Messrs.  Riehle  Bros.'  testing  machine;  the  others 
are  derived  from  various  sources.  Most  of  them  will  be  found  in 
the  articles  throughout  this  treatise. 


212 


STRENGTH  OF  BELTING  LEATHER 


Fig.  67, 


STRENGTH  OF  BELTING  LEATHER. 


213 


MATERIAL 
IN  BELT. 

SIZE  OF 
BELT 
TESTED. 

FORCE  BREAKING 
THE  BELT. 

FORCE  REQUIRED 
TO  BREAK  ONE 
INCH  WIDTH. 

FORCE  REQUIRED 
TO  BREAK  ONE 
SQUARE  INCH. 

REMAEKS. 

t 

11 
** 

|J 

H.S 

3 
3 
3 
3 
3 
3 
3 
3 

f 

3 
1 
2 
3 
2 
3 
1 
1 

it 

| 

Lbs. 
3750 
3625 
3500 
3375 
3250 
3000 
2250 
2875 
2000 
3500 
3000 
552 
1077 
1522 
1211 
1763 
530 
600 
1050 
1850 

Lbs. 
1250 
1208 
1166 
1125 
1083 
1000 
750 
958 
727 
1833 
1000 
552 
588 
507 
605 
587 
530 
600 
840 
1480 

Lbs. 
5000 
4833 
4666 
4500 
4333 
4000 
3000 
6131 
2909 

Centennial  Tests.    Oak  Tanned. 
n           «          « 

u              it             u 
It             11            11 
((             It            11 
tl                It               It 
tl                it               tl 
tl 
It 
It 
tl 

Mean  of  5  experiments  ord'y  leather. 

"       5          "              «          « 

«          q              tt                  it             n 
a          5              u                   it             it 
it          ~              u                  u             tt 

Oak  Tanned.                                 86* 
Page  Tannage.                               86 
Good  quality.     Many  tests.         86 
Good  quality.                                88 
English.     Kankine.                      82 
"       •           "                            82 
Good  new  English.                       54 

Towne.    American.                   163 
Ox.     English.     Kankine. 

1  G.  Spill  &  Co.,  London,  flax 
yarn  cemented.                      158 

London  Mech.  Mag.,  1863. 
Brazil         "           "          " 
White        "          "         " 
Russian      "           "          " 
Cord. 
Mech.  Mag.,  1863. 

CENTENNIAL  TESTS. 
|  "Union."     Two   shaved   leathers   with 
cloth  cemented  between.    No  rivets  in 
stronger  piece. 
Good  quality.                                 97 

ti 

n 

u 

tl 

Y 

It 

3\ 

A 

& 

T36 
T3* 

A 

11 

Kaw  Hide.... 
SugarTanned 
Rubber.  
"       3-ply 
Leather  

4571 
2944 

2872 
2705 

n 

n 

Kubber  3-ply 

«          « 

2836 

Rubber  3-ply 

Leather  
u 

it 

3200 
4000 
4278 
6417 
5000 

it 

a 

.    ».. 

Raw  Hide  ... 

1 
1 

3 

A 
A 

930 
1000 
2025 

« 
it 

1000 
675 

3086 
4200 

it 

Flax  

« 

5 
5 

... 

6272 
7448 
16632 
2100 

1254 
1489 
1663 
525 

it 
Leather  

10 
4 

... 

1890 
1610 
4000 
3200 
1680 
3981 

Sheep      "   .. 

Horse      "   .. 

«          tt  . 

it          it 

Cow         "  '.'. 
Cotton  Duck. 

Leather  

« 

u 

1 
3 
3 
1 

... 

200 
3000 
5625 

200 
1000 
1875 
1000 

These  figures  refer  to  the  Articles  from  which  the  tabular  numbers  are  taken. 


CHAPTER   VI. 
•  TRANSMISSION  OF  FORCE  BY  BELTS  AND  PULLEYS. 

By  Robert   Briggs,  accompanied   by  Experiments  of  Henry 

R.  Towne,  from  the  "  Journal  of  the  Franklin  Institute," 

January,  1868. 

161.  There  are  few  mechanical  engineers  who  have  not  been 
frequently  in  want  of  tabular  information  or  readily  applicable 
formulae,  upon  which  they  could  place  reliance,  giving  the  power 
which,  under  given  conditions  and  velocity,  is  transmitted  by  belts 
without  unusual  strain  or  wear.  The  formula  of  the  belt  or  brake 
is  well  known  and  simple,  and  it  is  only  necessary  to  acknowledge 
and  adopt  a  value  for  the  co-efficient  of  friction  (or  of  adhesion,  which 
is  perhaps  the  better  term),  to  allow  this  formula  to  be  applied  in 
daily  use.  And  this  co-efficient  of  friction  has  been  carefully  estab- 
lished by  the  experiments  of  General  Morin  and  M.  Prony,  and  has 
been  made  available  to  English  and  American  engineers,  by  the 
translation  of  Bennett.  * 

With  every  point  needed,  therefore,  at  the  command  of  the  engi- 
neer, it  is  somewhat  surprising  that  a  more  extensive  publication  and 
general  use  of  the  data  has  not  followed. 

But,  notwithstanding  the  existence  of  this  correct  mathematical 
and  experimental  information,  the  numerous  tables  which  have  been 
given  by  mechanical  engineers  appear  to  have  had  only  that  kind 
of  practical  basis  which  has  come  from  guessing  that  an  engine  or  a 
machine,  either  the  driving  or  the  driven,  with  a  belt  of  given  width, 
was  producing  or  requiring  some  quantity  of  power  which  might 
be  expressed  in  terms  (foot-pounds)  generally  without  any  stated 
arc  of  contact.  Three  rules,  given  by  practical  mechanics,  vary 
so  much  as  to  give  as  bases  for  estimate  (without  regard  to  arc 
of  contact)  0.76  horse-power,  0.93  horse-power,  and  1.75  horse- 

*  Bennett's  M&rin's  Mechanics,  New  York,  1860. 

It  must  be  remarked  that  there  are  some  mistakes  in  the  text  of  Bennett's 
translation,  which  will  lead  to  serious  errors,  unless  read  by  a  careful  investi- 
gator. 

214 


EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 


215 


power,  respectively,  for  the  power  of  a  belt  one  inch  wide  running 
1000  Fpm.* 

It  was  the  requirement  to  know  the  exact  useful  effect  of  a  novel 
disposition  involving  an  unusual  small  arc  of  contact  of  the  belt  upon 
the  pulley,  where  much  embarrassment  would  result  if  the  applica- 
tion proved  itself  unsatisfactory,  that  led  to  the  present  inquiry.  As 
the  writer  was  not  able  to  give  the  time  demanded  for  making  such 
experiments  as  would  establish  the  practical  co-efficient  of  adhesion, 
he  suggested  what  was  desired  to  Mr.  H.  R.  Towne,  and  the  numerous 
experiments,  of  which  he  gives  the  accompanying  report,  are  the 
result  of  his  labor  and  care. 

It  was  not  until  after  the  experiments  were  completed,  that  either 
Mr.  Towne  or  the  writer  knew  of  the  publication  of  M.  Prony  or 
General  Morin,  although  Bennett's  translation  rested  upon  the 
shelves  of  the  writer's  library  ;  but,  aside  from  the  gratification 
which  we  feel  at  the  corroboration,  we  think  the  reader  of  this 
article  will  be  pleased  to  know  that  our  data  is  founded  upon  the 
ordinary  pulleys  and  belts  of  the  workshop,  and  our  experiments 
were  not  impaired  by  any  niceties  which  common  workmen  would 
not  apply. 

Even  the  crudeness  of  our  experimental  apparatus,  and  the  gen- 
eral, not  over-exact,  method  adopted,  will  serve  to  demonstrate  to 
the  minds  of  practical  men  the  possibility  of  relying  upon  figures 
which  have  been  established  so  nearly  in  accordance  with  the  customs 
of  the  workshop. 

We  take  from  Rankiue's  Applied 
Mechanics  the  following  formula  of 
a  belt,  only  changing  the  words,  in 
the  hope  to  make  it  comprehensible 
to  the  general  reader  in  an  elemen- 
tary way: 

Let  A  be  a  pulley  upon  which 
the  belt  passes  from  T2  to  Tj.  Let 
r  =  the  length  of  radius  of  the  pul- 
ley A.  Let  T!  =  the  tension  of  the 
belt  (or  the  strain)  on  the  tight  side. 
Let  TU  —  the  tension  of  the  belt  (or  the  resistance  on  the  loose  side). 
Then  the  pull  on  the  belt  by  which  it  transmits  power  =  P  =  Tx  —  T2, 

*  It  will  be  shown,  by  the  deductions  from  experiments,  that  1.33  horse- 
power, nearly,  is  easily  given  in  continuous  work  by  a  belt  one  inch  wide  run- 
ning 1000  Fpm. 


Fig.  68. 


216          EXPERIMENTS    OF    ERIGGS    AND    TOWNE. 

and  this  difference  represents  the  adhesion  or  friction,  resulting  from 
the  contact  between  the  belt  and  the  pulley. 

If  we  suppose  the  tension  on  a  unit  of  width  of  belt  at  b  =  T2, 
then  it  follows  that  the  normal  pressure  per  unit  of  surface  at  the 

T 

point  b  =  —.    The  units  of  dimension,  either  linear  or  superficial, 

may  be  inches  and  square  inches,  feet  and  square  feet,  metres  and 
metres  square,  or  any  other  units  of  relative  value.  Thus  we  may 
say  the  normal  pressure  upon  a  square  inch  of  surface  at  b  equals  the 
tension  on  an  inch-wide  belt,  T2,  divided  by  the  length  in  inches  of 
the  radius,  r. 

We  will  endeavor  to  make  this  understood  by  comparing  the  case 
with  the  well-known  instance  of  the  relation  of  pressure  to  tension 
in  the  shell  of  a .  cylindrical  boiler.  If  we  take  an  example  of  a 
boiler  having  10  inches  radius  (or  20  inches  diameter),  and  with  an 
internal  uniform  pressure  of  100  Ibs.  per  square  inch,  it  will  be 
recognized  that  the  tangential  strain  per  inch  of  length  of  shell 
will  be  equal  to  the  pressure  multiplied  by  the  radius,  or  1000 
Ibs. ;  and  this  tangential  strain  is  uniform  at  all  points  of  the 
circumference. 

The  tension,  T2,  in  like  manner,  corresponds  to  the  tangential 
strain  just  stated,  and  the  resulting  normal  pressure  corresponds  to 
the  internal  uniform  pressure.  And  as,  in  the  instance  of  the  boiler, 
the  tangential  strain  is  exerted  at  all  points  of  the  circumference,  so 
the  normal  pressure  proceeding  from  the  tension  in  the  case  of  a  belt, 
is  independent  of  the  length  of  arc  of  contact  on  the  belt,  and  refers 
to  the  point  of  contact,  b,  wherever  that  point  may  be  taken  on  the 
pulley. 

T 

Admitting,  therefore,  that  the  pressure  at  the  point  b  =  — ,  we 


r 
have  the  friction  resulting  from  the  contact  of  the  belt  on  a  unit  of 

T 

surface  =f—  (when/  is  the  co-efficient  of  friction  of  the  leather  of 

the  belt  on  the  pulley).     This  gives  a  new  value  for  the  tension  of 
the  belt  at  some  point,  e  (very  near  6),  (or  tangential  strain  at  that 

rr\  -t 

point),  =  T2  -f  /—  =  T2  (l  +/  A     And  it  follows  that  the  pressure 

rp  -j 

atc=  —  (l  -}-/;,  and  the  friction  resulting  from  the  contact  of 
the  belt  on  a  unit  of  surface  =/  |— 2  (l  +/r)J»     This  again  gives 


EXPERIMENTS  OF  BBIGGS  AND  TOWNE.  217 
a  new  value  for  the  tension  of  the  belt  at  some  point,  d  (very  near 
«),  =  T2  +  /  [^  +  f~r  )]  =  T,  (l  +  £)•  On  taking  further 
points  in  succession,  until  we  take  I  points  and  reach  the  point  m  on 

1  rii 

the  figure,  we  have  for  the  tension  at  m  =  T2(l  +  /—")  =  T!  .*. -1 
?  \         v  /  I2 


This  equation  is  the  well-known  one  of  the  hyperbolic  logarithm. 

T         I      T         f- 
Where  hyperbolic  logarithm  ,=l  =/-  or  — l  =  e  r'  where  e  is  the  base 

^2  r  -1-2 

of  hyperbolic  logarithms.  We  can  further  transform  this  equation 
by  substituting  the  ratio  of  the  angle  in  degrees,  for  the  length  of 
contact  on  the  arc,  compared  to  the  radius. 

2rx  2rn         T          ~2*a 

Thus,  w   =  arc  of  1°,  let  l  =  a  (  .— )  .'.  ^  =  e 


and  taking  the  numerical  values  of  e,  *,  and  dividing  out  the  860, 

TJ_  _  &  718  0.017456  f  a 
'  T2~ 

•'•  %  (d)  = 


.-.log.  T<  —  log.  T2  =  0.00758 fa 

.   T1_w  0.00758 fa,  (2.) 


(3.) 


0.00758  a 


As  we  assumed  before,  P=  T,—  T2.     .:  T2=  Ti  —  P,  which  insert- 
ing in  equation  2. 

T,       _1Q0.00758fa 
'  ~ 


,.  P  (10    -*)  =  Tl  (10    - 

(4.) 


218          EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 

The  third  equation  is  the  one  to  which  we  would  now  call  atten- 

T 

tion.     By  it,  for  any  given  values  for  the  ratio  ^p1,  we  can  determine 

-1-2 

the  co-efficient  of  friction,  when,  by  experiment,  we  have  fixed  the 
greatest  difference  of  the  two  strains  without  slipping  on  a  pulley 
with  a  given  arc  (measured  by  a)  of  contact. 

We  would  here  make  a  very  important  observation,  which  forms 
the  key  of  the  whole  system  of  transmission  of  force  by  belts.  In 
practice,  all  belts  are  worked  at  the  maximum  co-efficient  of  friction.  A 
belt  may,  when  new  or  newly  tightened,  work  under  heavy  strain 
and  with  a  small  co-efficient  of  friction  called  into  action  ;  but  in 
process  of  time  it  becomes  loose,  and  it  is  never  tightened  again 
until  the  effort  to  perform  its  task  is  greater  than  the  value  of  the 
co-efficient  with  a  given  tension  of  belt,  and  the  belt  slips.  We  run 
our  belts  as  slack  as  possible,  so  long  as  they  continue  to  drive. 

It  has  been  shown  *  that  the  value  of  T!  -j-  T2,  or  the  sum  of  the 
strains  upon  the  two  sides  of  a  belt  (loose  and  tight),  is  a  constant 
quantity  ;  that  is,  when  a  belt  is  performing  work,  it  will  become 
loose  on  the  one  side  to  the  exact  amount  that  it  is  strained  on  the 
other,  and  when  at  rest,  not  transmitting  force,  the  tensions  will 
become  equal,  and  their  sum  be  the  same  as  before.  It  is  mani- 
fest that  the  limit  of  the  strength  of  a  belt  is  found  in  the  maximum 
tension  T!,  and  that  this  strength  being  known,  the  effective  pull  (P) 
is  further  limited,  with  any  given  arc  of  contact,  by  the  value/  of 
the  co-efficient  of  friction. 

The  discussion  has  so  far  been  limited  to  the  pull  exerted  by  a 
belt.  When  we  would  include  the  power  which  belts  will  transmit, 
we  have  only  to  multiply  the  pull  by  some  given  or  assumed  veloc- 
ity to  transform  our  equations  into  work  performed. 

By  means  of  the  third  equation,  we  will  now  deduce  a  value  for 
the  co-efficient  of  friction  as  given  by  the  experiments. 

All  the  experiments  were  with  the  arc  of  contact  =  180°  =  a, 

T 

which,  substituting  /—         T, 

1.8644 

and  the  result  of  168  separate  experiments  of  Mr.  Towne  has  given, 
under  tensions  of  T,  from  7  to  110  Ibs.  per  inch  of  width  of  belt: 


*  Bennett's  Morin,  page  303,  and  following  fl  252. 
f  Bennett's  Morin,  page  306,  fl  253,  gives  /=  0.573. 


EXPERIMENTS    OF    BRIGGS    AND    TOWNE.          219 

In  this  case  T!  has  in  all  cases  been  so  much  in  excess  of  T2  as  to 
slip  the  belt  at  a  defined,  slow,  but  not  accelerating  motion. 

From  an  examination  of  the  report  of  the  experiments,  we  think 
the  reader  will  coincide  with  our  conclusion  that  T%  of  this  value  of 

T 

—  -  can  be  taken  as  a  suitable  basis  for  the  working  friction  or  adhe- 

JU 

sion  which  will  cover  the  contingencies  of  condition  of  the  atmos- 

phere as  regards  temperature  and  moisture  ;  or 

^=3.7764  (maximum  practical  value)  .'./=fo 


2.0044 

The  experiments  further  show  that  200  Ibs.  per  inch  of  width  of 
belt  is  the  maximum  strength  of  the  weakest  part  —  that  is,  of  the 
lace  holes.  Taking  this,  with  a  factor  of  safety  at  one-third,  we  have 
the  working  strength  of  the  belt,  or  the  practical  value  for  T!  =  66| 
Ibs.f  The  case  when  belts  are  spliced  instead  of  laced,  a  great  in- 
crease of  strength  has  been  shown,  the  experiments  giving  380  Ibs. 
per  inch  of  width,  or  125  Ibs.  safe  working  strength. 

If  we  insert  these  values  of  /  and  T!  in  (4,) 


*  It  should  be  noted  that  the  experiments  were  made  without  any  appreciable 
velocity  of  belt,  and  throughout  this  paper  no  regard  has  been  paid  to  the  effect 
of  velocity  or  of  the  dimensions  of  the  pulleys  upon  the  value  of  the  coefficient 
of  friction. 

For  pulleys  less  than  12  inches  diameter  (with  the  belts  of  the  ordinary  thick- 
ness of  about  TVhs  inch),  and  for  velocities  exceeding  about  1000  Fpm,  allow- 
ance must  be  made  for  the  effect  of  centrifugal  force  in  relieving  the  pressure  of 
the  belt  on  the  pulley,  for  the  rigidity  of  the  belt,  and  for  the  interposition  of  air 
between  the  pulley  and  the  belt.  At  high  speeds,  say  3000  feet  velocity  of  belt  per 
minute,  the  want  of  contact  can  be  seen,  sometimes,  to  the  extent  of  one-third 
the  arc  encompassed  by  the  belt.  The  writer  has  proposed  to  place  a  de- 
flector or  stripper  near  the  belt,  to  take  off  the  stratum  of  air  moving  with  it, 
but  has  never  tried  the  experiment,  although  he  has  little  doubt  of  its  giving 
some  advantage. 

f  Bennett's  Morin,  page  306,  fl  253,  gives  55.1  Ibs.  per  inch  of  width  as  admis- 
sible. 

J  This  equation  (5)  is  the  really  important  one  in  practice,  and  by  means  of 
logarithms  can  be  solved  for  any  values  of  a°  readily  ;  but  as  some  of  those  who 
may  wish  to  use  it  may  not  be  at  once  prepared  to  use  the  logarithmic  notation, 


220 


EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 


The  largest  possible  angle  for  an  open  belt,  without  a  carrier  or 
tightener,  is  180°,  as  upon  either  the  driving  or  the  driven  pulley 
this  cannot  be  exceeded;  but  for  crossed,  or  carried,  or  tightened 
belts,  the  angle  may  be  as  large  as  270°. 

We  give  the  following  table  of  results  for  different  arcs  of  contact 
(corresponding  to  a°)  within  the  usual  limits  of  practice. 

Table  I.       . 

Strain  transmitted  by  belts  of  one  inch  width  upon  pulleys,  when  the  arcs 
of  contact  vary  as  the  angles  of 


90° 

100° 

110° 

120° 

135° 

150° 

180° 

210° 

240° 

270° 

Lbs. 
32.33 

Lbs. 
34.80 

Lbs. 
37.07 

Lbs. 
39.18 

Lbs. 
42.06 

Lbs. 
44.64 

Lbs. 
49.01 

Lbs. 
52.52 

Lbs. 
55.33 

Lbs. 
57.58 

If  we  suppose  the  pulley  to  be  one  foot  in  diameter,  and  to  run 
some  number,  N.  of  Rpm,  we  have  the  power  transmitted  =  N*P. 

from  want  of  use  or  practice,  we  give  an  example.  Suppose  we  take  an  angle 
of  90°,  the  negative  exponent  then  becomes  —  0.003206  X  90  =  —  0.28854  ;  sub- 
tracting this  from  1,  we  have  —  1.71146.  This  term  thus  becomes  10  —1-71146. 
Now  this  expression  is  only  the  notation  for  anti-logarithm  —  1.71146,  or  in 
words  the  number  for  which  —  1.71146  is  the  logarithm.  Logarithmic  tables 
give  this  number  =  0.51505,  and  the  equation 


P= 


,  —  0.003206  X  90\  =  66j  ^  _  10 

1(1  —  0.51505}  =  66JX  0.4S495. 
:.P=32.S3. 


EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 


221 


And  we  give  the  following  table  for  different  arcs  of  contact  (cor- 
responding to  a°)  within  the  usual  limits  of  practice. 

Table  II. 

Power  transmitted  by  belts  on  pulleys  one  foot  in  diameter  one  Rpm. 
Arcs  of  contact  of  belts  upon  pulleys  corresponding  to  the  angles. 


INCHES  OF 
WIDTH 
OF  BELT. 

90° 

100° 

110° 

120° 

135° 

150° 

180° 

210° 

240° 

270° 

Foot-lbs 

Foot-lbs 

Foot-lbs 

Foot-lbs 

Foot-lbs 

Foot-lbs 

Foot-lbs 

Foot-lbs 

Foot-lbs 

Foot-lbs 

1 

102 

109 

116 

123 

132 

140 

*154 

165 

174 

181 

2 

203 

219 

233 

246 

264 

280 

308 

330 

348 

361 

3 

305 

328 

349 

369 

396 

420 

462 

495 

521 

542 

4 

406 

437 

466 

492 

528 

560 

616 

660 

695 

723 

5 

508 

547 

582 

615 

660 

701 

770 

825 

869 

904 

6 

609 

656 

699 

738 

792 

841 

924 

990 

1043 

1084 

7 

711 

766 

815 

861 

924 

982 

1078 

1155 

1217 

1265 

8 

813 

875 

932 

985 

1056 

1122 

1232 

1320 

1391 

1446 

9 

914 

984 

1048 

1108 

1188 

1262 

1386 

1485 

1564 

1626 

10 

1016 

1094 

1165 

1231 

1321 

1402 

1540 

1650 

1738 

1807 

The  application  of  Table  II.  to  any  given  cases  of  known  angle 
of  the  arc  of  contact,  width  of  belt  in  inches,  diameter  of  pulley  in 
feet,  and  number  of  revolutions,  is  simply  to  take  the  figures  from 
the  table  for  the  first  two,  and  multiply  by  the  two  succeeding  con- 
ditions, to  obtain  the  foot-lbs.  of  power  transmitted. 

We  have  taken  the  following  examples :  —  First.  Mr.  Schenck  (of 
New  York)  found  an  18-inch  wide  belt  running  2000  Fpra,  the  pul- 
leys being  16  feet  to  6  feet,  would  give  40  horse-power,  with  ample 
margin  (one-fourth).  (Sic.) 

If  we  take  the  distance  from  centre  of  the  16-feet  pulley  to  that 
of  the  6-feet  to  be  25  feet  (about  the  usual  way  of  placing  the  fly- 
wheel pulley  of  an  engine  in  regard  to  the  main  line  of  shafting),  we 
have  the  arc  of  contact  subtending  about  153°.  From  Table  I.  the 
strain  transmissible  is  45.1  Ibs.  x  18  x  2000  =  1,623,600  foot-lbs.  = 
49.2  horse-power. 

Second.  Mr.  William  B.  Le  Van  (of  Philadelphia)  found  by  indi- 
cator that  an  18-inch  wide  belt  running  1800  Fpm,  the  pulleys  being 
16  feet  and  5  feet  respectively,  transmitted  43  horse-power,  with 
maximum  power  transmissible  unknown.  If  we  take  the  centre's 

*A  1-foot  pulley,  1  inch  wide,  running  215  Kpm,  gives  1  horse-power. 


222          EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 

distance,  as  before,  at  25  feet,  we  have  the  arc  of  contact  subtending 
about  150°. 

From  Table  I.  we  derive  44.64  Ibs.  as  the  strain  transmissible  x 
18  x  1800  =  1,446,336  foot-lbs.  =  43.83  horse-power.  The  same  au- 
thority found  by  indicator  that  a  7-inch  wide  belt  over  two  2-feet 
6-inch  pulleys,  11  feet  centre  to  centre  (horizontal),  moving  942 
Fpm,  gave  8  horse-power.  From  Table  I.  for  180°  angle,  we  take 
49.01  x  7  X  942  =  323,172  foot-lbs.  =  9.79  horse-power.  This  belt 
was  stated  to  be  very  tight. 

Third.  Mr.  A.  Alexander  (London  Engineer,  March  30th,  1860) 
gives  a  rule  that  a  1-inch  belt  will,  at  1000  feet  velocity,  transmit 
Ij  horse-power. 

If  we  take  the  contact  at  180°  from  Table  I.,  49.01  X  1000  = 

49.000  foot-lbs,  we  have  only  IJ  horse-power. 

Fourth.  Mr.  William  Barbour  (same  journal,  March  23,  1860) 
gives  as  the  power  a  1-inch  belt  will  transmit  with  1000  feet  veloc- 
ity =  0.927  horse-power,  when  we  derive  with  180°  angle  from  our 
tables  =  1^  horse-power. 

Fifth.  A.  B.  Ex  (same  journal,  April  6,  1860)  gives  a  rule 

diameter  in  inches  x  Rpm  X  breadth  in  inches 

5000 

ratio  of  pulleys  not  to  exceed  5  to  1.     Changing  this  rule  to 

diameter  in  feet  X  Rpm  X  width  in  inches       ,T  ,    ,  „ 

— — =N  foot-lbs. 

5000  +  12  +  33,000 

Diameter  in  feet  x  Rpm  x  width  in  inches 

o.oms  - 

.'.  79.2  x  diameter  in  feet  X  Rpm  x  width  in  inches  =  N.  foot-lbs. 

From  Table  II.  the  angle  of  120°  gives  123  in  place  of  79.2,  and 
it  would  appear  this  authority  adopts  about  f  the  effect  we  take. 

Sixth.  Dr.  Fairbairn  gives  (Mills  and  Mill  Work,  Part  II.,  page 
4)  a  table  of  approximate  width  of  leather  straps  in  inches  necessary 
to  transmit  any  number  of  horses-power,  the  velocity  of  the  belt 
being  taken  at  25  to  30  feet  per  second  (1500  to  1800  per  minute), 
one-foot  pulley,  3.6  inches  wide,  gives  one  horse-power. 

Assume  1650  Fpm,  contact  180°,  we  have,  from  Table  I.,  1650  X 

49.01  X  3.6  X  1  =  29,112  foot-lbs.  =  0.87  horse-power. 

Seventh.  Kankine  gives  (Rules  and  Tables,  page  241)  0.15  as  the 


EXPERIMENTS    OF    BKIGGS    AND    TOWNE.          223 

co-efficient  of  friction,  probably  applicable  to  the  adhesion  of  belts 
on  pulleys,  to  be  used  with  his  formulae  in  estimating  the  power 
transmitted.  Neither  experiments  nor  practice  give  so  small  a  co-effi- 
cient as  this. 

We  could  multiply  authorities  on  these  points,  but  think  the  cor- 
roboration  of  those  we  quote  with  our  tables  sufficient  to  establish 
our  experimental  and  estimated  co-efficient  of  friction,  /=  0.423,  as 
a  proper  practical  basis. 

We  give  the  two  following  cases  not  only  to  show  the  application 
of  the  formula  5,  but  as  matters  of  some  interest. 

In  the  construction  of  one  of  the  forms  of  centrifugal  machines 
for  removing  water  from  saturated  substances,  the  main  or  basket 
spindle  is  driven  by  cone-formed  pulleys,  one  of  which,  being  covered 
with  leather,  impels  the  other  by  simple  contact. 

In  the  particular  instance  taken,  the  iron  pulley  on  the  spindle 
was  6  inches  largest  diameter,  and  the  leather-covered  driving  pulley 
was  12  inches  largest  diameter  ;  the  length  of  cones  on  the  face  was 
4  inches,  this  last  dimension  corresponding  to  width  of  belt  in  other 
cases.  By  covering  the  leathered  pulley  with  red  lead  we  were  able 
to  procure  an  impression  on  the  iron  pulley,  showing  the  width  of 
the  surfaces  of  contact  when  the  pulleys  were  compressed  together 
with  the  force  generally  applied  when  the  machine  was  at  work. 
This  width  was,  at  the  largest  diameters,  almost  exactly  |  of  an  inch. 
From  the  nature  of  the  two  convex  surfaces  compressing  the  leather 
between  them,  the  actual  surface  of  efficient  contact  cannot  be  taken 
at  over  half  this  width  (the  slight  error  in  estimating  this  contact  as 
straight  lines  in  place  of  circular  arcs  may  be  neglected).  This  gives 
the  angle  subtended  by  the  arc  of  contact  on  the  iron  pulley  =  2^°, 
taking  equation  (5). 


V  —  iQ—1:991985)  =00  J  ^  _  0  tgs171)  =  QQ\  (0.01829}  =  1.3717. 

Now,  the  average  diameter  of  the  iron  pulley  in  the  middle  of  its 
4-inch  face  is  4.708  inches  =  0.3923  feet,  with  a  circumference  of 
1.2326  feet,  and  it  is  usual  to  run,  at  the  least  velocity,  1000°  Kpm  ; 
whence  the  power  given  by  these  pulleys  =  1.3717  Ibs.  X  4  inches 
X  1.2326  feet  X  1000  revolutions  =  6757  foot-lbs.  —  I  horse-power. 
As  the  work  performed  by  one  of  these  centrifugal  machines  is 
the  acquirement  of  velocity  under  the  resistance  of  the  friction  of 


224          EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 

the  machine  and  of  the  air,  and  the  work  of  expelling  the  moisture 
is  so  insignificant,  in  comparison,  that  it  may  be  neglected  in 
estimating.  It  can,  therefore,  be  taken  as  probable  that  the  real 
power  demanded  to  keep  the  machine  in  motion  is  very  nearly  that 
given  by  calculation.  It  should  be  stated  that  the  basket  belonging 
to  this  particular  machine  is  29  inches  diameter  and  12  inches  deep. 

The  second  special  case  we  instance  at  present  consists  in  a  pro- 
posed arrangement  for  driving  a  fan  which  had  previously  been  found 
to  demand  an  8-inch  belt  on  a  10-inch  pulley  to  run  it  1275  Rpm. 
(The  arc  of  contact  here  was  162°,  so  that  the  apparent  power,  with 
a  very  tight  belt,  was  37  A  horse-power;  but  about  ^  of  this  was 
defective  adhesion  from  running  a  rigid  belt  over  so  small  a  pulley.) 
It  was  thought  desirable  to  avoid  the  fast-running  countershafts,  and 
drive  this  direct  from  an  engine-pulley  fly-wheel,  by  impingement, 
so  to  speak,  of  the  belt  on  its  tight  side  between  the  fan-pulley  and 
another  larger  carrier  pulley,  against  a  portion  of  the  periphery  of 
the  fly-wheel. 

If  we  suppose  the  force  demanded,  measured  on  the  fan-pulley  as 
before,  to  be  40  horse-power  =  1,320,000,  and  the  fan-pulley  to  be  10 
inches  diameter  X  16  inches  wide,  and  to  run  1250  Rpm, 

1  ^20  000 

.-.—  -  —  =  25.2  as  the  pull,  P,  on  each  inch  of  width  of 

1250  x  |g  x  16  x  * 

the  belt  as  it  comes  from  the  10-inch  pulley.  By  substituting  this 
value  for  P  in  equation  (5),  and  then  reducing  the  equation  to  find 
the  value  for  a°,  we  have  a°  =  65°,  which  is  the  angle  of  contact 
demanded  to  give  the  necessary  adhesion. 

It  will  be  noticed  that  this  angle  is  independent  of  the  diameter 
of  the  fly-wheel  pulley,  it  being  only  requisite  that  that  diameter 
should  be  such  as,  with  the  given  or  assumed  number  of  revolutions, 
will  produce  the  given  velocity.  In  the  case  taken  for  example,  the 
fly-wheel  pulley  was  16  feet  diameter  x  16  inches  wide,  with  70  Rpm 
velocity. 

As  we  have  before  remarked,  the  sum  of  the  two  tensions  on  the 
belt  is  constant,  whether  the  belt  is  performing  work  or  not  ;  that  is, 


As  we  assumed  in  equation  (5)  T  to  equal  66|  Ibs.,  we  can  substitute 
the  value  of  P  as  in  Table  I.,  in  the  equation,  S  =  2  (66|)  —  P  = 
133|  —  P,  from  which  it  is  evident  that  the  sum  of  the  tensions  will 
vary  with  P  or  with  the  angle  of  contact.  It  is  evident,  also,  that 


EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 


225 


the  load  upon  the  shaft  proceeding  from  the  tensions  T2  and  Tj  will 
be  the  resultant  of  whatever  angle  the  belt  makes  with  a-line  joining 
the  centres  of  the  two  pulleys,  or  as  the  cosine  of  that  angle. 

By  constructing  on  paper  a  pair  of  pulleys,  it  will  be  readily  dis- 
cerned that  the  angle  in  question  for  small  pulleys  =  90°  — ,  and  for 

« 

large  and  crossed  ones,  =  ^  —  90°,  we  can  consequently  form  the  fol- 
lowing table : 

Table  III. 

STRENGTH   OF   LACING   OF   JOINT   66J    POUNDS   PER   INCH   WIDE, 

Showing,  first,  the  sum  of  tensions  on  both  sides  of  a  belt,  per  inch  of 
width,  whether  in  motion  or  at  rest,  when  strained  to  transmit  the 
maximum  quantity  of  power  in  general  practice;  and  showing, 
second,  the  load  carried  by  the  shafts  and  supported  constantly  by 
the  journals  per  inch  of  width  of  belt,  when  the  arcs  of  contact  vary 
as  the  angles  of 


1st, 
2d, 

90° 

100° 

110° 

120° 

135° 

150° 

180° 

210° 

240° 

270° 

Lbs. 
101. 
71.42 

Lbs. 

98.53 
75.47 

Lbs. 
96.26 

78.85 

Lbs. 
94.15 
81.53 

Lbs. 
91.27 
84.32 

Lbs. 

88.69 
85.67 

Lbs. 
84.32 
84.32 

Lbs. 

80.81 
78.05 

Lbs. 
78. 
67.59 

Lbs. 
75.75 
53.56 

When  machinery  is  driven  by  gearing,  the  shafts  only  carry  the 
running  wheels  and  the  weight,  and  when  the  machines  are  thrown 
on,  the  friction  of  the  lines  increases  with  the  work ;  but  with  belts 
and  pulleys  the  load  on  the  line  and  its  frictional  resistance  is  con- 
stant, whether  the  machinery  works  or  lies  idle. 

Of  course,  it  is  not  proper  to  assume  that  the  load  produced  by 
the  belt  on  the  shaft  is  exactly  that  given  by  the  second  line  in 
Table  III. ;  but  we  can  be  safe  in  taking  those  weights  as  rarely 
exceeded,  because  belts  begin  to  fail  when  they  are ;  and  as  rarely 
much  less,  because  few  of  our  machines  are  not  worked  up  to  their 
belt  capacity. 

The  advantages  shown  by  the  figures  on  all  the  tables,  but  espe- 
cially on  the  last,  in  those  arcs  of  contact  over  180°  where  crossed 
belts  are  used,  have  the  substantial  ground  of  practice,  although 
many  mechanics  are  unaware  of  the  facts.  The  writer  will  instance 
a  case  of  several  heavy  grindstones  having  from  main  to  counter 
lines  8-inch  crossed  belts  on  pulleys  3  feet  diameter,  running  120  rev- 
15 


226          EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 

olutions,  only  8  feet  centre  to  centre,  where  belts  have  already  lasted, 
day  and  night  use,  3^  years.  For  the  same  purpose,  6-inch  open 
belts  were  formerly  used  with  an  average  duration  of  a  few  weeks 
only. 

Another  use  of  a  crossed  belt  is  for  long  belts,  the  crossing  effec- 
tually preventing  those  waves  which  generally  impair,  if  they  do  not 
destroy,  such  belts  when  open. 

Besides  the  actual  power  transmitted  by  belts,  which  it  has  here 
been  attempted  to  embrace  in  a  general  law — the  application  of 
belting  —  both  the  manner  and  the  purpose  opens  a  field  for  dis- 
cussion far  beyond  the  limits  of  the  present  article,  the  writer 
hoping  that  others  will  take  up  the  subject,  so  that  the  published 
data  of  the  mechanic  may  more  fully  include  the  practice  of  the 
workshop  and  factory. 

Note  to  the  above  Article. 

162.  The  folio  wing  addition  to  the  preceding  paper  may  afford 
some  facility  in  the  use  of  the  results.  The  figures  are  derived  from, 
and  the  final  results  correspond  to,  the  figures  given  in  Table  II. 

When  the  arc  of  contact  of  a  belt  upon  the  least  of  2  pulleys 
which  it  connects  is 

90°    100°    110°    120°    135°    150°    180°    210°    240°  270° 
then 

3900  3600    3400    3200    3000    2825    2570    2400    2280   2190 

is  the  sum  of  the  multiplication  together  of  the  inches  of  diameter 
of  the  pulley  by  the  inches  of  width  of  the  belt,  by  the  number  of 
Rpm  which  equal  one  horse-power.  Or  to  make  the  use  of  this  per- 
fectly clear  we  give  the  following  rule :  To  find  the  horse-power  of 
33,000  Ibs.  lifted  one  foot  high  in  one  minute  given  out  by  certain 
belt,  pulley,  and  speed.  Multiply  the  inches  of  diameter  of  pulley 
by  the  inches  width  of  belt  and  by  number  of  Rpm,  and  divide  the 
result  by  the  numbers  given  in  the  last  line  of  figures  as  relating  to 
the  contact  the  belt  has  on  the  smaller  of  its  pulleys,  and  the  quo- 
tient will  be  the  number  of  horse-power. 

Machine  tools,  lathes  and  boring  tools,  require  to  be  belted  3  times 
as  strongly  as  the  average  use  in  work,  to  overcome  occasional  resist- 
ance and  starting  frictions. 


EXPERIMENTS    OF    BRIGGS    AND    TOWNE.         227 

On  the  Adhesion  of  Leather  Belts  to  Cast-Iron  Pulleys, 
by  Henry  R.  Towne. 

163.  The  following  experiments,  undertaken  at  the  instance  of 
Mr.  Robert  Briggs,  had  for  their  object  to  determine,  in  a  satisfac- 
tory and  conclusive  manner,  the  true  value  of  the  co-efficient  of  fric- 
tion of  leather  belts  on  cast-iron  pulleys.  This  result  has,  it  is  hoped, 
been  attained,  and  in  the  preceding  article  Mr.  Briggs  has  discussed 
at  length  the  theory  of  the  action  of  belts,  and  has  also  given  prac- 
tical formulae  in  which  the  co-efficient  of  friction  employed  is  that 
deduced  from  these  experiments,  which  latter  have  been  made  with 
great  care,  and  may,  it  is  believed,  be  accepted  as  reliable.  In  order, 
however,  that  all  interested  may  judge  for  themselves  of  the  correct- 
ness of  the  deductions  made  from  them,  we  present  herewith  a  com- 
plete tabular  record  of  the  experiments,  which  will  also  repay  exam- 
ination as  exhibiting  several  interesting  and  instructive  facts  con- 
nected with  the  efficiency  of  leather  belts. 

The  experiments  were  made  with  leather  belts  of  3  and  6  inches 
width,  and  of  the  usual  thickness  —  about  T3^ths  of  an  inch.  The 
pulleys  used  were  respectively  of  12,  23-|,  and  41  inches  diameter, 
and  were  in  each  case  fast  upon  their  shafts.  They  were  the  ordinary 
cast-iron  pulleys,  turned  on  the  face,  and,  having  already  been  in  use 
for  some  years,  were  fair  representatives  of  the  pulleys  usually  found 
in  practice. 

Experiments  were  made  first  with  a  perfectly  new  belt,  then  with 
one  partially  used  and  in  the  best  working  condition,  and,  finally, 
with  an  old  one,  one  which  had  been  so  long  in  use  as  to  have  dete- 
riorated considerably,  although  not  yet  entirely  worn  out.  The  adhe- 
sion of  the  belts  to  the  pulleys  was  not  in  any  way  influenced  by  the 
use  of  unguents  or  by  wetting  them  —  the  new  ones  when  used  were 
just  in  the  condition  in  which  they  were  purchased  —  the  others  in 
the  usual  working  condition  of  belts  as  found  in  machine-shops  and 
factories  —  that  is,  they  had  been  well  greased  and  were  soft  and 
pliable. 

The  manner  in  which  the  experiments  were  made  was  as  follows : 
The  belt  being  suspended  over  the  pulley,  in  the  middle  of  its  length, 
weights  were  attached  to  one  side  of  the  belt,  and  increased  until  the 
latter  slipped  freely  over  the  pulley;  the  final,  or  slipping  weight, 
was  then  recorded.  Next,  5  Ibs.  were  suspended  on  each  side  of  the 
belt,  and  the  additional  weight  required  upon  one  side  to  produce 
slipping  ascertained  as  before,  and  recorded.  This  operation  was 


228          EXPERIMENTS    OF    BKIGGS    AND    TOWNE. 

repeated  with  10,  20,  30,  40,  and  50  Ibs.,  successively,  suspended  upon 
both  sides  of  the  belt.  In  the  tables  these  weights,  plus  half  the 
total  weight  of  the  belt,  are  given  as  the  "  equalizing  weights  "  (T2 
in  the  formulae),  and  the  additional  weight  required  upon  one  side  to 
produce  slipping,  is  given  under  the  head  of  "  unbalanced  weights ; " 
this  latter,  plus  the  equalizing  weight,  gives  the  total  tension  on  the 
loaded  side  of  the  belt  (Tl  in  the  formulas). 

The  belt,  in  slipping  over  the  pulley,  moved  at  the  rate  of  about 
200  Fpm,  and  with  a  constant,  rather  than  increasing,  velocity ;  or, 
in  other  words,  the  final  weight  was  such  as  to  cause  the  belt  to  slip 
smoothly  over  the  pulley,  but  not  sufficient  to  entirely  overcome  the 
friction  tending  to  keep  the  belt  in  a  state  of  rest.  In  this  case  (i.  e. 
with  an  excessive  weight)  the  velocity  of  the  belt  would  have  approx- 
imated to  that  of  a  falling  body,  while  in  the  experiments  its  velocity 
was  much  slower,  and  was  nearly  constant,  the  friction  acting  pre- 
cisely as  a  brake.  By  being  careful  that  the  final  weight  was  such 
as  to  produce  about  the  same  velocity  of  the  slipping  belt  in  all  of 
the  experiments,  reliable  results  were  obtained. 

It  became  necessary  to  make  use  of  a  weight  such  as  would  pro- 
duce the  positive  motion  of  the  belt  described  above,  as  it  was  found 
impossible  to  obtain  any  uniformity  in  the  results  when  the  attempt 
was  made  to  ascertain  the  minimum  weight  which  would  cause  the 
belt  to  slip.  With  much  smaller  weights  some  slipping  took  place, 
but  it  was  almost  inappreciable,  and  could  only  be  noticed  after  the 
weight  had  hung  for  some  minutes,  and  was  due  very  probably  to  the 
imperceptible  jarring  of  the  building.  After  essaying  for  some  time 
to  conduct  the  experiments  in  this  way,  and  obtaining  only  conflicting 
and  unsatisfactory  results,  the  attempt  was  abandoned,  and  the  experi- 
ments made  as  first  described. 

In  this  way,  as  may  be  seen,  results  were  obtained  which  compare 
together  very  favorably,  and  which  contain  only  such  discrepancies 
as  will  always  be  manifest  in  experiments  of  the  kind.  It  is  only  by 
making  a  great  number  of  trials  and  averaging  their  results,  that 
reliable  data  can  be  obtained. 

The  value  of  the  co-efficient  of  friction  which  we  deduce  from  our 
experiments,  is  the  mean  of  no  less  than  168  distinct  trials. 

It  will  be  noticed,  however,  that  the  co-efficient  employed  in  the 
formulae  is  but  T60  of  the  full  value  of  that  deduced  from  the  experi- 
ments, the  latter  being  0.5853  and  the  former  0.4229.  This  reduc- 
tion was  made,  after  careful  consideration,  to  compensate  for  the 
excess  of  weight  employed  in  the  experiments  over  that  which  would 


EXPERIMENTS    OF    BBIGGS    AND    TOWNE.         229 

just  produce  slipping  of  the  belt,  and  may  be  regarded  as  safe  and 
reliable  in  practice. 

A  note  is  made,  over  the  record  of  each  trial,  as  to  the  condition 
of  the  weather  at  the  time  of  making  it  —  whether  dry,  damp,  or 
wet  —  and  it  will  be  noticed  that  the  adhesion  of  the  belts  to  the 
pulleys  was  much  affected  by  the  amount  of  moisture  in  the  atmos- 
phere. It  is  to  be  regretted  that  this  contingency  was  not  provided 
for,  and  a  careful  record  of  the  condition  of  the  atmosphere  kept  by 
means  of  a  hygrometer.  The  experiments  indicate,  clearly,  however, 
that  the  adhesion  of  the  old  and  the  partially-used  belts  was  much 
increased  in  damp  weather,  and  that  they  were  then  in  their  maximum 
state  of  efficiency.  With  the  new  belts  the  indications  are  not  so 
positive ;  but  their  efficiency  seems  to  have  been  greatest  when  the 
atmosphere  was  in  a  dry  condition. 

Experiments  were  also  made  upon  the  tensile  strength  of  belts, 
with  the  following  results :  The  weakest  parts  of  an  ordinary  belt  are 
the  ends  through  which  the  lading  holes  are  punched,  and  the  belt  is 
usually  weaker  here  than  the  lacing  itself.  The  next  weakest  points 
are  the  splices  of  the  several  pieces  of  leather  which  compose  the  belt, 
and  which  are  here  perforated  by  the  holes  for  the  copper  rivets. 
The  strengths  of  the  new  and  the  partially-used  belts  were  found  to 
be  almost  identical.  The  average  of  the  trials  is  as  follows : 

Three-inch  belts  broke  through  the  lace-holes  with 629  Ibs. 

"       rivet    "        "    1146   " 

"      solid  part    "    2025   " 

These  give  as  the  strength  per  inch  of  width. 

When  the  rupture  is  through  the  lace-holes 210  Ibs. 

rivet    "    382   " 

solid  part 675   « 

The  thickness  being  ^  inch  (—  .219),  we  have  as  the  tensile 
strength  of  the  leather  3086  Ibs.  per  square  inch. 

From  the  above  we  see  that  200  Ibs.  per  inch  of  width  is  the  ulti- 
mate resistance  to  tearing  that  we  can  expect  from  ordinary  belts. 

The  experiments  herein  described  are  strikingly  corroborative  of 
those  already  on  record,  and  this  gives  increased  assurance  of  their 
reliability ;  and,  although  there  is  nothing  novel  either  in  them  or  in 
their  results,  it  is  hoped  that  they  will  prove  of  interest,  and  that  an 
examination  of  them  will  lead  to  confidence  in  the  formulae  which 
are  based  upon  them. 


230 


EXPERIMENTS    OF    BRIGGS    AND    TOWNE. 


Three-Inch  New  Belt. 


ON  12-INCH  PULLEY  (BETWEEN  SEAMS). 


ON  12-INCH  PULLEY  (ON  SEAMS). 


ll 

S-3 

e«'C 


cedW 
ge  of  T 


'Soi 


111 


2.94 
7.94 
12.94 
22.94 
32.94 
42.94 
52.94 


Dmp. 
17 
43 

70 
108 
124 
159 
210 


Dry. 

20 

58 

86 
167 
226 
311 
343 


18.5 
50.5 
78.0 
137.5 
175.0 
235.0 
276.5 


21.44 

58.44 

90.94 

160.44 

207.94 

277.94 

329.44 


7.29 
7.36 
7.03 
699 
6.31 
6.47 
6.22 


2.94 
7.94 
12.94 
22.94 
32.94 
42.94 
52.94 


Dmp. 
14 
30 

48 

92 
107 
134 
191 


Dmp. 
14 
32 

51 
87 
110 


14.0 
31.0 
49.o 
89.5 
108.5 
136.0 


38.94 
62.44 
112.44 
141.44 
178.94 
242.44 


5.76 
4.90 
4.83 
4.90 
4.29 
4.17 
4.58 


Mean....  ...  6.810 


Mean, 


4.775 


Three-Inch  New  Belt. 


ON  23%-INCH  PULLEY. 

ON  41-INCH  PULLEY. 

fa 

iff 

ed  Weight, 
No.  1. 

ed  Weight, 
L  No.  2. 

If 

ss 

•g's 

Height  on 
ide  of  Belt 
5lt  Slipped 

=  T! 

Ti 

t|  = 

*S    §  £r™ 

^^2H 

«£2  " 

L 

ed  Weight, 
I  No.  2. 

Ii 

£H 
•go 

Is®  * 

>s^ 

T, 

i|ii 

•SSa 

ss 

ri  - 
1H 

c.S 

1s 

II 
sj 

p-oBpS  H 

T2 

!!!§ 

ll 

c.S 

3* 

II 

.0  gJ 

^cc«  II 
'S'ga 
o-g® 

T2 

&** 

i 

c 

^  O   fe 

o*  *"*  ^ 

a 

s 

^   O  ^ 

w° 

p 

P 

p4** 

^ 

w  ° 

p 

p 

p^ 

J 

Dmp. 

Dmp. 

Dry. 

Dry. 

2.94 

12 

16 

14.0 

16.94 

5.76 

2.94 

13 

13 

13.0 

15.94 

5.42 

7.94 

34 

44 

39.0 

46.94 

5.91 

7.94 

38 

39 

38.5 

46.44 

5.85 

12.94 

54 

77 

65.5 

78.44 

6.06 

12.94 

55 

61 

58.0 

70.94 

5.48 

22.94 

110 

135 

1225 

14544 

634 

2294 

32.94 

161 

191 

176.0 

208.94 

6.34 

32.94 

188 

176 

182.0 

214.94 

6.53 

4294 

207 

234 

2205 

26344 

6  14 

4294 

52.94 

277 

282 

279.5 

332.44 

6.28 

52.94 

289 

295 

292.0 

344.94 

6.52 

Meat 

6.118 

Mean. 

5.960 

Three-Inch  Belt. 


PARTIALLY  USED  AND  IN  GOOD  ORDER  —  ON  12-INCH  PULLEY. 

-2s 
»fl  o  **-* 

§ 

§ 

bo 

i 

§ 

il 

§11 

'3  c  ®  « 

1* 

ft 

^d 

^6 

jf  0 

ge 

iSojf  . 

TI 

bo^*  II 

'g^ 

'S^ 

"S  $25 

"3^5 

^^ 

^  o 

"S'd^H 

fill 

Jl 

.11 

II 

C3 

ll 

II 

-si  a  " 

T2 

2*5  B 

JH 

^H 

2 

^gH 

c5  ^> 

O^j 

ws° 

3 

a 

c 

c 

fi 

gf 

Ho^ 

3.2 

Damp. 
13 

Damp. 
14 

Wet. 

26 

Dry. 
12 

D7. 

15.5 

18.7 

5.84 

8.2 

34 

36 

53 

32 

32 

37.4 

45.6 

5.56 

13.2 

57 

63 

77 

50 

50 

59.4 

72.6 

5.50 

23.2 

102 

109 

149 

90 

99 

109.8 

133.0 

5.73 

33.2 

123 

128 

226 

144 

144 

153.0 

186.2 

5.61 

43.2 

174 

185 

299 

183 

210.2 

253.4 

5.87 

53.2 

226 

265 

338 

249 



268.5 

322.7 

6.07 

Mean  :  

5.754 

EXPERIMENTS    OF    BRIGGS    AND    TOWNE.         231 

Three-Inch  Belt  —  Partially  Used  and  in  Good  Order 


ON  41-INCH  PULLEY. 

ON  23%-INCH  PULLEY. 

fli- 

balanced Weight, 
Trial  No.  1. 

balanced  Weight, 
Trial  No.  2. 

balanced  Weight, 
verage  of  Trials. 

'otal  Weight  on 
aded  Side  of  Belt 
hen  Belt  Slipped 
=  T2. 

. 

m 

T^ 

ualizing  Weights, 
Initial  Tension 
>n  each  Side  of 
Belt  =  T2. 

balanced  Weight, 
Trial  No.  1. 

balanced  Weight, 
Trial  No.  2. 

balanced  Weight, 
Trial  No.  3. 

balanced  Weight, 
Terage  of  Trials. 

otal  Weight  on 
ided  Side  of  Belt 
len  Belt  Slipped 

T8 

ts 

p 

a 

!§« 

3* 

W° 

a 
P 

a 
p 

a 

g* 

3* 

Dry. 

Dry. 

Dmp. 

Dmp. 

Dry 

3.2 

26 

25 

25.5 

28.7 

8.97 

3.2 

23 

22 

23 

22.6 

25.8 

8.06 

8.2 

59 

55 

57.0 

65.2 

7.95 

8.2 

53 

54 

53 

53.3 

61.5 

7.50 

13.2 

86 

82 

84.0 

97.2      7.36 

13.2 

86 

89 

82 

85.6 

98.8 

7.48 

23.2 

2^9 

141 

33.2 

188 

194 

190.5 

223.7      6.74 

33.2 

194 

210 

181 

195.6 

228.2 

6.87 

43.2 

.     1 

432 

293 

53.2 

306 

323 

314.5 

367.7      6.91 

53.2 

285 

316 

272 

291.0 

344.2 

6.47 

Mea 

a.... 

7.586 

Mea 

7.276 

Three-Inch  Old  Belt. 


ON  12-INCH  PULLEY. 


g  Weights, 
Tension 
Side  of 
=  T2. 


fi 

ss 


ON  23%-INCH  PULLEY. 


I- 
^ 

II 


T2 


2.75 
7.75 
12.75 
22.75 
32.75 
42.75 
52.75 


Dmp, 

12 

35 

61 
102 
142 
203 
259 


Dmp 

13 

39 

66 
109 
158 
220 
273 


12.5 
37.0 
63.5 
105.5 
150.0 
211.5 
266.0 


15.25 
44.75 

76.25 
128.25 
182.75 
2.54.25 
318.75 


5.55 
5.77 
5.98 
5.64 
5.58 
5.95 
6.04 


2.75 
7.75 
12.75 
22.75 
32.75 
42.75 
52.75 


Dmp, 

16 

48 

72 
157 
220 
256 
301 


Wet. 

20 

70 
106 
174 
232 
276 
311 


18.0 

59.0 

89.0 

165.5 

226.0 

271.0 

306.0 


20.75 
66.75 
101.75 
188.25 
258.75 
313.75 
358.75 


7.55 
8.61 
7.98 
8.27 
7.90 
7.34 
6.80 


Mean 5.787 


Mean 7.778 


Six-Inch  New  Belt. 


ON  23%-INCH  PULLEY. 


•23-gs 


P 

a 
p 


ON  41-INCH  PULLEY. 


til* 


6.75 
11.75 
16.75 
26.75 
36.75 
46.75 
56.75 


Dry. 

30 

53 

78 
125 
161 
216 
265 


Dmp. 

36 

63 

81 
135 
177 
223 


269   267.0 


39.75 
67.75 
96.25 
156.75 
205.75 
266.25 
323.75 


5.89 
5.77 
5.75 
5.86 
5.60 
5.70 
5.70 


6.75 
11.75 
16.75 
26.75 
36.75 
46.75 
56.75 


32 
53 

72 
118 
159 
209 
265 


29 

50 

72 

115 

176 

236 

275 


37.25 
7325 

88.75 
143.25 
204.25 
269.25 
326.75 


5.52 
6.23 
5.30 
5.36 
5.55 
5.76 
5.76 


Mean. 


5.752 


5.640 


CHAPTER   VII. 

EXPERIMENTS  ON  THE  TENSION  OF  BELTS, 
MADE  AT  METZ  IN  THE  YEAR  1834. 

BY    ARTHUR   MORIN. 

Translated  by  J.  W.  HUTTINGEE,  Member  of  the  Franklin  Institute,  Philada. 

Determination  of  the  Natural  Tension  of  Belts. 

104.  There  remains,  then,  nothing  more  than  to  indicate  how 
we  have  been  able,  for  each  series  of  experiments,  with  the  same 
relative  disposition  of  the  axes  of  rotation,  with  the  same  hygro- 
metric  state  of  the  belt,  to  determine  the  sum  of  the  tensions  t  and  if. 

There  are  for  this  several  simple  means,  but  we  have  usually 
employed  the  following.  When  the  apparatus  was  in  place,  com- 
pletely set  up  and  put  in  motion,  and  when  we  were  thus  assured 
that  the  belt  had  sufficient  tension  to  overcome  the  resistance,  we 
commenced  a  series  of  experiments,  during  the  continuation  of  which 
we  did  not  change  the  distance  of  the  axles  ;  the  variation  of  the 
tension,  or  the  lengthening  of  the  belt,  could  then  not  take  place, 
except  by  a  state  more  or  less  hygrometric.  The  apparatus  worked 
thus  :  the  belt  did  not  slip  on  the  pulley,  as  long  as  the  resistance 
offered  by  the  journals  was  not  too  great  ;  but  if,  by  not  oiling,  it 
happened  that  the  resistance  increased  to  such  an  extent  that  the  belt 
began  to  slip,  the  shaft  ceased  to  turn  with  continuity,  and  as  the 
dynamometer  showed,  nevertheless,  a  curve  of  flexion  corresponding 
to  the  difference  of  the  tension  at  the  moment  ;  we  have  to  determine 
t  and  t'  the  two  simultaneous  relations  : 


7?  ' 

t  =  ife       ,       (t  —  t')  R  =  FL  +  0,413  +  0,0078  t  -f  0,0082  ^,* 

by  means  of  which  we  can  determine  t  and  t',  and  consequently 
t  +  1f=  2  T. 

It  is  by  observations  of  this  kind  that  one  has  usually  determined,  at 
each  different  position  of  the  apparatus  in  relation  to  the  wheel,  the 
natural  tension  of  the  belt.  Although  the  relative  displacement  of  the 

*  Let  t  =  natural  tension,  t'=  t  -f-  friction  of  belt  on  drum.  All  the  figures  are 
given  according  to  the  metric  system,  and  the  comma  is  used  for  decimal  point. 

232 


EXPERIMENTS    OF    A.    MORIN.  233 

axes  would  evidently  exercise  the  principal  influence  upon  the  natural 
tension,  nevertheless  we  must  assure  ourselves  if  the  very  perceptible 
variations,  which  the  hygrometric  state  of  the  belt  proved,  had  not 
also  a  notable  influence  upon  this  tension,  and  to  take  it  into  account, 
if  not  with  exactness,  at  least  with  a  close  approximation.  This  belt 
runs  over  the  drum,  d  d,  Fig.  69,  close  to  the  wheel,  which  we  had 
taken  the  precaution  to  cover  with  a  light  roof,  that  it  might  not 
become  too  wet  and  get  out  of  centre ;  but,  as  it  passed  very  near  to 
the  wheel,  it  was  not  possible  that,  during  the  rapid  movement  of  the 
latter,  to  prevent  its  becoming  wet  by  the  throwing  off  of  water 
which  the  floats  constantly  raised.  Further,  the  belt,  which  at 
the  beginning  of  each  day  was  dry,  or  very  nearly  so,  was  at  the  close 
almost  completely  wet.  There  resulted  from  this  two  different  effects, 
which,  relatively  to  the  speed  of  the  machine  and  to  the  employment 
of  belts  under  like  circumstances,  nearly  balanced  each  other.  The 
first  is,  that  the  belt  lengthened  in  such  a  manner  that  its  natural 
tension  diminished ;  the  second  is,  that  the  ratio  of  the  friction  to  the 
pressure  of  the  belt  and  the  pulley  increased  notably,  and  con- 
sequently the  limit  at  which  the  belt  would  slip  was  being  reached  by 
the  first  effect,  and  was  receding  by  the  second. 

It  was  necessary,  then,  at  each  of  the  observations  made,  to  deter- 
mine the  tension  of  the  belt,  to  examine  if  it  were  dry  or  wet,  in 
order  to  take  into  calculation  the  proper  value  of  the  relation,/,,  of 
the  friction  to  the  pressure. 

Special  Observations  to  Determine  the  Natural  Tension. 

160.  There  remain  to  be  given  the  results  of  observations  made, 
to  apply  the  preceding  methods  to  different  series  of  experiments, 
which  I  shall  do  in  order. 

The  apparatus  was  completely  set  up,  and  began  to  work  on  the 
8th  of  August,  and,  from  that  day  to  the  17th  of  the  same  month, 
inclusive,  it  occupied  the  same  place ;  the  belt  was  but  lit.tle  stretched, 
and-  it  was  frequently  observed  that  when  it  was  damp  it  slipped 
when  the  curve  of  flexion  of  the  spring  corresponded  to  the  scale  of 
loss,  with  an  effort  of  26k,50,  brought  to  bear  upon  the  circumference 
of  the  pulley  with  a  radius  of  Om,308,  we  have  then 

FL  =  26k,50  x  Om, 308  =  8, 162, 
in  this  case.     (See  Tables  II.  and  III.) 

f,=  0,377,     e  =  2,71828,     log.  e  =  0,43429,         = 


234  EXPERIMENTS    OF    A.    MORIN. 

By  means  of  these  statements  we  deduce  from  the  two  preceding 
equations 

t'=  13k,67,       t  =  3,1421!  =  43k,95,       t  +  t'  =  2  T=  56k,62. 


From  the  18th  of  August  the  apparatus  was  moved  a  little  further 
off,  the  belt  was  tightened  till  the  28th,  inclusive,  the  dry  belt  slipped 
when  the  curve  of  flexion  corresponded  to  the  scale  with  an  effort  of 
36k,75,  applied  to  the  circumference  of  the  pulley  ;  we  have  then 

FL  =  36k,75  x  (^,308  =  11,319; 
we  had  besides 

/,  =  0,282  (see  Table  II.), 

the  other  statements  are  the  same,  and  we  deduce  from  the  two  equa- 
tions employed 

t'  =  3(^,08,      t  =  2,354tr  =  70",  81,       t  +  t'=2  T=  10&£9. 

From  the  3d  to  the  7th  of  November,  a  time  at  which  the  abun- 
dance of  water  permitted  me  to  recommence  the  experiments  which  the 
dryness  and  other  occupations  had  compelled  me  to  suspend,  the  belt 
being  slack  and  damp,  I  found  that  it  slipped  when  the  curve  of  flex- 
ion indicated  upon  the  scale  of  loss  an  effort  of  17  kilogrammes 
brought  to  bear  upon  the  circumference  of  the  pulley  ;  we  have  then 

FL  =  IT  ,00  x  0,308  =  5,236,        /,  =  0,377, 
from  which  we  deduce 

t'  =  9k,01,        t  =  3,142  t'  =  28k,30,        t  +  t'=2  T=  37\31. 

From  the  8th  November  to  the  12th,  inclusive,  when  the  experiments 
were  terminated,  the  belt  having  been  overstretched  by  moving  the 
axles  too  far  off,  we  determined  the  natural  tension  by  another  means, 
employed  at  the  beginning  and  at  the  end  of  the  day,  or,  in  other 
words,  when  the  belt  was  dry  and  when  it  was  wet,  which  is  shown 
in  No.  37  of  Section  III.  of  M.  Poncelet's  "  Course  of  Mech."  (See 
Art.  178.)  The  cast-iron  shaft  being  stopped,  and  the  sluice-gate 
closed  in  such  a  way  that  the  least  water  possible  could  enter,  we 
immediately  placed  upon  the  horizontal  front  (up-stream)  float  of  the 
water-wheel  the  amount  of  weight  necessary  to  drive  the  wheel  and 
make  the  belt  slip  upon  the  cast-iron  pulley  ;  but  as  a  little  water 
passed  continually,  which  rose  to  a  certain  height  on  the  wheel,  it 
was  necessary  to  repeat  the  experiment  in  an  inverse  order  by  placing 


EXPERIMENTS    OF    A.    MORIN.  235 

the  weights  upon  the  horizontal  back  (down -stream)  float,  till  the 
wheel  moved  again.  By  taking  the  mean  reckoning  of  the  2  weights 
we  compensated  the  effect  of  the  water,  because  it  acted  in  an  oppo- 
site direction  in  the  2  cases,  and  we  had  nothing  to  do  but  to  estab- 
lish the  relation  of  equilibrium  between  the  2  weights,  the  friction 
of  the  wheel  upon  its  journals,  and  the  difference  of  the  tensions  at 
the  moment  of  slipping  upon  the  cast-iron  pulley.  Then  calling : 

8  =  the  weight  which  turned  the  wheel. 

R  =  lm,85,  the  mean  radius,  including  the  floats. 

R'=  Om,514,  the  mean  radius  of  the  pulley  mounted  on  the  shaft, 

including  the  half-thickness  of  the  belt. 
JV^^the  pressure  upon  the  journals  of  the  wheel. 
/"=  0,08,  the  ratio  of  friction  to  the  pressure  for  the  journals  and 

their  bearings,  with  lard  as  lubricator. 
p    =  Om,03,  the  radius  of  the  journals. 

M=  1587  kilogrammes,  the  weight  of  the  wheel  and  its  shaft. 
t,  t',  a  and  a'  retain  the  same  significations  and  values  as  below.* 

We  had  at  the  moment  of  slipping  £S 

F) 

(t  —  f)  R'+fN#  =  8R,  and  t  =  t'e 

(  Oy96  (M-t  cos.  a-t'  cos.  a')  \  =0,96  M- 0,396 1'- 0,293 1, 
\        +  0,4  (t  sin.  a  +  t'  sin.  a')  j 

and  consequently 

(*—  0  #'+  0,96f"M?  —  0,396f"t'?  —  0,293f"t<>  =  SE. 

The  observations  made  when  the  belt  was  dry  have  shown  that  it 
slipped  under  the  action  of  a  weight  of 

S=15  kilogrammes; 
we  had  already  (see  Tables  II.  and  III.) 

£  =  0,282,        t  =  2,354  t', 

and  we  have  deduced  from  the  substitution  in  the  above  formula 
H  =  34\76,         t  =  81*  £25,         t  +  t'  =  116\58. 

*  t  =the  tension  of  the  conducting  strip  of  the  belt. 
t'=  the  tension  of  the  conducted  strip. 

a  =  51°.     a'  =  45°,  the  angles  which  these  tensions,  t  and  t' ,  make  respec- 
tively with  the  vertical. 


236  EXPERIMENTS    OF    A.    MORIN. 

Other  observations,  made  when  the  belt  was  wet,  have  given 

S=  18,50  kilogrammes ; 
we  had  (see  Tables  II.  and  III.) 

f  r\  9'V'y 

from  which  we  deduced 

f  -=  27*, 85,  t  =  87k,50,  t  +  t'  =  115*, 85. 

These  last  two  series  of  experiments  show  that,  when  the  belt  is 
stretched  tight  enough,  the  difference  of  tension  produced  by  the 
hygrometic  lengthening  is  very  little ;  and  taking  the  mean  of  the 
values  of  t  +  £',  obtained  under  extreme  circumstances,  between 
which  all  the  results  of  the  same  day  necessarily  come  in,  when  the 
belt  has  passed  successively  from  a  state  of  dryness  to  that  of  complete 
saturation,  we  see  that  the  difference  of  this  mean  t  +  t'=  115k,96, 
for  each  of  the  extreme  values,  is  only  about  3^  of  its  real  value. 

This  result  is  sufficient  for  the  calculation  of  our  experiments, 
since  it  shows  that  having  determined  the  sum  of  the  tensions  in 
the  case  when  the  belt  was  dry,  or  in  that  when  it  was  wet,  it  will 
be  allowed,  without  fear  of  an  appreciable  error,  to  regard  it  as 
very  nearly  constant  and  equal  to  the  value  found  in  one  or  the 
other  case,  which  dispenses  with  many  special  observations. 

But  there  are  more,  and  it  is  easy  to  see  that,  in  our  apparatus,  and  in 
consequence  of  its  dimensions  and  use,  a  considerable  variation  in  the 
tension  of  the  belt  could  have  only  a  very  slight  influence  in  many  cases. 

In  effect,  the  formula  (see  note  on  page  237), 

comes  back  to  FL+fW=fNr, 

FL  =  0,96  fQr  —  0,96 fpr'—  (0,915 1  +  0,961 1'}  (fr'—fr\ 

in  which  it  is  evident  that  the  influence  of  the  terms  t  and  t'  will  be 
as  much  less  as  /  and  r  shall  differ  less  than  fr' ,  and  it  would  be  zero 
if  we  had/'=/  and  /=  r,  which  is,  however,  evident  a  priori.  Now, 
in  many  experiments,  r  does  not  differ  from  r'  but  by  J,  and  for  all 
cases  where  the  surfaces  are  oily  we  have,  very  nearly,  f=f. 

This  observation  shows  that,  if  it  be  necessary  to  take  the  results 
of  experiments  on  the  tension  of  the  belt  into  calculation,  the  slight 
variations  which  it  can  show,  in  consequence  of  its  hygrometric  state, 
are  without  notable  influence,  and  that  it  is  sufficient  to  have  deter- 
mined the  natural  tension  for  each  position  at  some  time  during  the 
series  of  experiments,  as  I  have  done.  As  to  the  rest,  one  can  assure 
himself  directly  that  in  admitting,  in  the  natural  tension,  a  variation 
|  to  £,  which  much  exceeds  what  observation  has  shown,  the  value  of 


EXPERIMENTS    OF    A.    MORIN.  237 

the  ratio /given  by  the  formula  below*  would  not  change  ^,  which 
may  be  disregarded  by  comparison  with  the  real  difference  which 
resistance  offers. 

The  result  of  values  found  at  different  times  for  the  natural  ten- 
sion of  belts  which  we  have  employed  for  the  calculation  of  the  ratio 
of  friction  to  the  pressure. 

From  the  8th  to  the  17th  of  August,  included,  the  formula 

FL  +  Of  66 
~  (0,96  Q  +  53,10)r 
From  the  18th  to  the  28th  of  August,  included,  the  formula 

FL  +  1,220 
~(0,96Q  +  94,63}r 

From  the  3d  to  the  7th  of  November,  included,  the  formula 
.          FL+0,711 

il2tl 
/  — 


From  the  8th  to  the  12th  of  November,  included,  the  formula 

FL  +  1,341 

(0,96Q~+  108,77)r 


*  Q  =  the  total  charge  of  the  shaft,  including  its  own  weight,  that  of  all  the 
dynamometric  apparatus  of  the  pulley  of  the  journals,  and  of  the  discs. 

p  =  50  k,  the  weight  of  the  pulley. 

F  =  the  tension  of  the  spring. 

L  =  its  lever-arm,  in  relation  to  the  axle  of  the  shaft. 

J2  =  0m,308,  the  exterior  radius  of  the  pulley,  including  the  half  thickness 
of  the  belt. 

r  =  the  radius  of  the  journals. 

r'  =  Om,06,  the  radius  of  the  eye  of  the  pulley. 

f  —  the  ratio  of  the  friction  to  the  pressure  for  the  journal  and  the  box. 

//=the  same  ratio  for  the  iron  eye  of  the  pulley  and  the  cast-iron  shaft. 
We  have  found  it  equal  0,144. 

N=  the  pressure  exercised  by  the  journals  of  the  shaft  upon  their  bearings. 

N'=ihe  pressure  exercised  by  the  pulley  upon  the  shaft. 

It  is  easy  to  see,  from  what  we  have  said  above,  that  between  the  tensions  t 
and  i'  ',  the  tension  F  of  the  spring,  and  the  friction  of  the  pulley  upon  the  shaft, 
one  will  have  the  relation 


and  that  between  the  friction  of  the  journals  upon  their  boxes,  the  tension  F  of 
the  spring,  and  the  friction  of  the  eye  of  the  pulley  on  the  shaft,  one  will  have 

FL-\-f'N'r'=fNr; 

FL+f'N'r' 
whence  we  deduce  /—    -  —  -  • 


238  EXPERIMENTS    OF    A.    MOBIN. 

Verifications  of  Two  Theorems  Employed  to  Prove  the  Preceding 

Formulae. 

166.  By  means  of  the  formulae  which  I  have  just  given,  it  is 
easy  to  calculate  the  results  of  experiment,  but  they  are  based,  as  we 
have  seen,  upon  two  mechanical  theorems,  which,  although  based  on 
principles  exempt  from  all  supposition  of  agreement  with  the  manner 
in  which  belts  ought  to  act,  appear  to  me  to  need  the  proof  of  experi- 
ment in  order  that  the  deductions  which  I  have  made  might  be 
guarded  against  all  uncertainty.     This  induced  me  to  mal$e  special 
experiments  upon  the  friction  of  belts  upon  wooden  drums  and  cast- 
iron  pulleys,  and  upon  the  manner  in  which  their  tension  varies  from 
wood  to  iron.     I  will  give  an  account  of  them  by  commencing  with 
the  premises. 

Experiments  upon  the  Slipping  of  Belts  upon  Cast-iron  Pulleys. 

167.  Three  wooden  drums,  with  diameters  of  Om,836,  Om,408, 
Om,100,  were  successively  employed   for  these  experiments.      They 
were  placed  horizontally  in  a  fixed  position  in  such  a  manner  that 
they  could  not  turn,  and  over  them  was  passed  a  belt  of  black  curried 
leather,  almost  new,  but  having  acquired  a  certain  softness  by  the 
use  which  we  had  made  of  it  in  the  previous  experiments.     Its 
breadth  was  Om,050,  with  a  thickness  of  Om,0053 ;  its  rigidity  appeared 
so  feeble,  that  we  were  justified  in  disregarding  it,  in  its  ratio  to  the 
friction  on  the  surface  of  the  drum.     The  two  strips  of  the  belt  hung 
vertically  in  equal  portions  on  each  side  of  the  drum,  and  to  each 
one  of  them  was  attached  the  platform  of  a  balance  to  receive  the 
weights.     The  belt  weighed  2k,295,  each  platform  of  the  balance 
Ok,229,  consequently  the  weight  of  each  strip  of  the  belt  of  equal 
length  was  lk,376 ;  the  arc  embraced  was  equal  to  the  semi-circum- 
ference;  we  then   placed  equal  weights   into  each   platform,  then 
gradually  added  to  one  of  them  weights  enough  to  make  the  belt 
slip  on  the  drum.     We  see,  by  this,  that  the  tension  t'  of  the  ascend- 
ing strip  was  equal  to  lk,376,  plus  the  weight  contained  in  the  cor- 
responding platform,  and  that  the  tension  t  of  the  descending  strip 
was  equal  to  tf  plus  the  weight  added  above  the  first  load.     Finally, 
the  slipping  of  the  belt  took  place  perpendicularly  to  the  fibres  of 
the  wood. 


EXPERIMENTS    OF    A.    MOBIN. 


239 


Order  of  the  Following  Tables. 

108»  These  details  are  sufficient  to  give  an  idea  of  the  mode  of 
experiment  adopted,  and  nothing  remains  but  to  add  the  table  of 
results : 

Table  No.  I. 

Experiments  upon  the  Friction  of  Belts  upon  Wooden  Drums. 


No.  OF  EX- 
PERIMENTS. 

WIDTH 

OF 

BELT. 

CONDITION 
OF  BELT. 

DIAM- 
ETER OF 
DRUM. 

LENGTH 

OF 

ARC  EM- 
BRACED. 

TENSION 

RATIO 

OF 

FRICTION 

TO 

PRESSURE 

OF  AS- 
CENDING 
STRIP. 

OF  DE- 
SCENDING 
STRIP  OR 
MOTOR. 

. 

| 

M. 

M. 

M. 

Kilogram. 

Kilogram. 

1 

0,050 

0,836 

1,313 

6,376 

30,376 

0,497 

2 

0,050 

0,836 

1,313 

6,376 

29,376 

0,486 

3 
4 
5 

6 

0,050 
0,050 
0,050 
0,050 

Dry,  or 

somewhat 
unctuous. 

0,836 
0,836 
0,836 
0,836 

1,313 
1,313 
1,313 
1,313 

6,376 
16,376 
16,376 
16,376 

29,876 
75,876 
69,526 
68,676 

0,492 

0,488 
0,460 
0,458 

7 

0,050 

0,836 

1,313 

11,376 

50,376 

0,473 

8 

0,050 

0,836 

1,313 

11,376 

43,376 

0,426 

Mean  — 

0,472 

9 

0,050 

0,408 

0,640 

6,376 

26,876 

0,472 

10 

0,050 

Dry,  or 

0,408 

0,640 

6,376 

31,376 

0,458 

11 

0,050 

somewhat 

0,408 

0,640 

6,376 

28,676 

0,507 

12 

0,050 

unctuous. 

0,408 

0,640 

16,376 

63,876 

0,479 

13 

0,050 

0,408 

0,640 

16,376 

63,876 

0,433 

Mean.... 

0,462 

14 

0,050 

0,100 

0,157 

6,376 

33,376 

0,526 

15 

0,050 

0,100 

0,157 

6,376 

34,376 

0,541 

16 

0,050 

Dry, 

0,100 

0,157 

11,376 

41,376 

0,411 

17 

0,050 

somewhat 

0,100 

0,157 

11,376 

44,876 

0,438 

18 

0,050 

unctuous. 

0,100 

0,157 

11,376 

42,876 

0,422 

19 

0,050 

0,100 

0,157 

16,376 

73,376 

0,477 

20 

0,050 

0,100 

0,157 

16,376 

76,436 

0,490 

Mean.... 

0,472 

21 

0.028 

0,836 

1,313 

5,401 

32,401 

0,570 

22 

0,028 

0,836 

1,313 

5,401 

32,901 

0,575 

23 

0,028 

Very  dry 

0,836 

1,313 

10,401 

51,901 

0,512 

24 

0,028 

and  rough. 

0,836 

1,313 

10,401 

47,401 

0,483 

25 

0,028 

0,836 

1,313 

15,401 

62,401 

0,446 

26 

0,028 

0,836 

1,313 

15,401 

61,901 

0,443 

Mean.... 

0,504 

240  EXPERIMENTS    OF    A.    MOKIN. 

Observations  on  the  Results  contained  in  the  Preceding  Table. 

169.  In  comparing  with  each  other  the  values  of  the  ratio  /,  of 
the  friction  with  the  pressure  of  the  belt  upon  the  surface  of  the  oak 
drum  deduced  from  the  formula 


R  2,3026  l      t 

t  =  te  orf,=  —g—  log.  -  , 

R 

in  which  —  expresses  the  semi-circumference  of  a  circle  equal  to  *  = 

3,1416,  where  the  logarithms  are  those  given  in  tables,  which  brings 
us  back  to  the  form 

f,  =  0,733  log.  ^ 

under  which  it  has  been  employed  in  the  calculations,  we  see  that 
these  values  are  sensibly  constant,  and  that  the  particular  mean  de- 
duced from  each  of  the  first  three  series  is  the  same  at  ^  nearly, 
although  the  extent  of  the  arc  embraced,  or  the  diameter  of  the 
drum  may  vary  in  the  proportion  of  8  to  2  and  to  1,  about,  and 
that  the  tensions  may  have  nearly  reached  the  limits  usually  given 
to  belts  in  machines.  These  three  series  of  experiments  plainly  con- 
firm, then,  the  theory  adopted  and  assigned  to  the  ratio  /,  of  the  fric- 
tion to  the  pressure  for  new  belts,  but  soft  and  even,  slipping  upon 
oak  drums  perpendicularly  to  the  fibres  of  the  wood,  the  mean  value 
f,=  0,470. 

This  value,  deduced  from  twenty  experiments,  is  much  less  than 
was  concluded  from  the  experiments  of  1831,  which  gave  us  the 
value  0,74  as  the  ratio  of  friction  of  smooth  surfaces  of  curried 
leather  upon  oak,  the  movement  being  parallel  to  the  fibres  of  the 
wood,  and  after  a  prolonged  contact  ;  but  the  compressed  state  of  the 
leather  being  entirely  different  in  the  two  cases,  it  appears  to  me 
that  this  display  of  results  is  not  surprising. 

As  to  the  fourth  series  of  experiments  contained  in  this  table,  and 
which  relates  to  the  friction  of  a  belt  entirely  new  and  very  rough, 
which  for  more  than  8  years  dried  in  a  garret,  they  assign  also  to 
the  ratio  /,  a  constant  value  but  a  little  more  than  the  preceding, 
which  can,  without  doubt,  be  attributed  to  the  condition  of  the  rub- 
bing surface  of  the  leather.  We  will  observe,  besides,  that  this  belt 
had  only  a  breadth  of  Om,028,  or  about  half  the  size  of  the  preceding. 
This  last  series  confirms,  as  to  belts,  the  law  of  the  independence  of 
surfaces. 


EXPERIMENTS    OF    A.    MORIN. 


241 


170.    Table  No.  II. 

Experiments  upon  the   Friction  of  Curried  Leather  Belts  upon  Cast-iron 

Pulleys. 


No.  OF 
EXPERIMENT. 

WIDTH 

OF 

BELT. 

CON- 
DITION 

OF 

BELT. 

DIAM- 
ETER OF 
PUL- 
LEY. 

LENGTH 

OF 

ARC  EM- 
BRACED 

TENSION 

RATIO 

OF 

FRIC- 
TION TO 
PRES- 
SURE. 

OBSERVATIONS. 

OF  AS- 
CENDING 
STRIP. 

OF  DE- 
SCENDING 
STRIP  OR 
MOTOR. 

M. 

M. 

M. 

K. 

K. 

2 
3 
4 

0,050 
0,050 

0,050 
0,050 

Dry  or 
some- 
what 

n  Tiof* 

0,610 
0,610 

0,610 
0,610 

0,958 

0,958 
0,958 
0,958 

6,376 

6,376 
6,376 
16,376 

13,476 
16,776 
15,776 
29,276 

0,238 
0,308 
0,288 
0,301 

This  belt  was  old, 
and  had  long  been 
used  in  a  spinning- 
mill. 

5 

0,050 

unct- 

0,610 

0,958 

16,376 

40,376 

0,282 

6 

0,050 

UOUS. 

0,610 

0,958 

16,376 

37,376 

0,262 

Mean.. 

0,279 

7 
8 

0,050 
0,050 

Dry  or 

0,610 
0,610 

0,958 

0,958 

6,376 
11,376 

16,000 

27,876 

0,300 
0,285 

This  belt  was  new, 

9 
10 
11 

0,050 
0,050 
0,050 

some- 
what 
unct- 

0.610 
0,610 
0,610 

0,958 
0,958 
0,958 

11,376 
16,376 
16,376 

25,876 
36,376 
36,376 

0,271 
0,254 
0,254 

and  had  been  em- 
ployed but  a  very 
short  time  in  the  ex- 
periments upon  the 
friction  of  journals. 

12 

0,050 

uous. 

0,610 

0,958 

26,376 

72,876 

0,323 

Mean.. 

0,281 

13 

14 
15 

0,050 
0,050 
0,050 

Dry  or 

some- 

0,110 
0,110 
0,110 

0,173 
0,173 
0,173 

6,376 
6,376 
11,376 

14,376 
18,376 
26,876 

0,259 
0,336 
0,273 

The  pulley  had 
been  turned,  and 
its  breadth  was  only 

16 
17 

0,050 
0,050 

what 
unct- 

0,110 
0,110 

0,173 
0,173 

11,376 
16,376 

30,876 
36,876 

0,318 
0,259 

Om,  03,  which  reduced 
the  rubbing  surface 
of  the  belt  to  Om,  03. 

18 

0,050 

uous. 

0,110 

0,173 

16,376 

36,876 

0,259 

Mean.. 

0,284 

19 

0,050 

0,610 

0,958 

11,376 

30,876 

0,317 

20 

0,050 

Humid 

0,610 

0,958 

6,376 

19,876 

0,361 

21 

0,050 

and 

0,610 

0,958 

6,376 

19,876 

0,361 

22 

0,050 

much 

0,610 

0,958 

16,376 

51,876 

0,366 

23 

0,050 

wet. 

0,610 

0,958 

16,376 

57,876 

0,401 

24 

0,050 

0,610 

0,958 

21,376 

90,376 

0,458 

Mean.. 

0,377 

16 


242  EXPERIMENTS    OF    A.    MORIN. 

Experiments  upon  Curried  Leather  Belts  upon  Cast- Iron  Pulleys. 

171.  The  experiments  upon  the  friction  of  curried  leather  belts 
upon  cast-iron  pulleys  were  made  in  a  like  manner  as  the  preceding. 
The  pulleys  employed  were,  first,  that  of  the  apparatus  described  in 
No.  1  and  following,  whose  breadth  of  Om,10  was  double  that  of  the 
belt.     Its  surface  was  slightly  convex,  and  had  not  been  turned  after 
being  cast,  but  it  was  nearly  a  true  circle,  with  a  diameter  of  Om,610. 
Secondly,  a  little  pulley,  having  a  diameter  of  Om,110,  and  a  breadth 
of  Om,030,  and  consequently  narrower  than  the  belt,  which,  having  a 
breadth  of  Om,050,  projected  Om,010  at  one  side  or  the  other:  its  sur- 
face, turned  and  polished,  was  slightly  convex. 

The  belt  was  then  used  dry,  and  in  an  unctuous  state,  as  it  was 
left  by  the  tanner,  with  two  dry  pulleys,  then  entirely  saturated  with 
water,  and  the  large  pulley  also  wet.  The  other  data  of  exper- 
iments and  the  arrangements  of  the  table  are  shown  the  same  as  in 
preceding  experiments,  and  it  is  superfluous  to  enter  into  further 
details. 

Observations  upon  the  Results  contained  in  the  Preceding  Table. 

172.  The  examination  of  the  results  stated  in  the  preceding 
table  completely  confirm  those  of  Table  I.,  and  the  theory  adopted. 
We  see  that,  in  effect,  as  well  as  in  extent  of  the  arcs  embraced, 
the  diameter  of  the  pulleys  may  vary  nearly  in  the  ratio  of  6  to  1, 
the  breadth  of  the  belt  pressing  upon  the  pulley  in  that  of  2  to  1,  and 
the  tension  in  that  of  1  to  3  on  the  one  part,  and  of  1  to  6  on  the 
other,  the  value  of  /,  remained  sensibly  constant  and  in  the  mean 
equal  for  the  dry  belt  upon  dry  pulleys,  let 

f,=  0,282. 

When  the  belt  is  wet,  as  well  as  the  pulley,  the  ratio  increases  and 
becomes  in  the  mean 

f,=  0,377. 

These  are  the  two  values  which  we  have  adopted  at  the  beginning  of 
this  essay  and  following  for  the  calculation  of  the  tensions  of  the  belt 
in  our  apparatus. 

By  recapitulating  the  results  of  these  two  series  of  experiments 
upon  the  friction  of  belts  upon  wooden  drums,  or  upon  cast-iron 
pulleys,  one  can  see  that  we  are  justified  in  concluding  therefrom 
that  the  ratio  of  this  resistance  to  the  pressure  is : 

1st.   Independent  of  the  breadth  of  the  belt,  and  of  the  developed 


EXPERIMENTS    OF    A.    MORIN.  243 

length  of  the  arc  embraced,  or  of  the  diameter  of  the  drum,  or  what 
amounts  to  the  same  thing,  independent  of  the  surface  of  contact. 

2d.  Proportional  to  the  angle  subtended  by  the  belt  at  the  surface 
of  the  drum. 

3d.  Proportional  to  the  logarithm,  Naperian  or  hyperbolic,  of  the 
ratio  of  the  tensions  of  the  two  strips  of  the  belt. 

Experiments  upon  the  Variation  of  the  Tension  of  Belts : 
Description  of  the  Apparatus. 

173.  Let  us  now  pass  to  the  experiments  which  have  had  for 
their  end  the  verification  of  the  law  of  the  variation  of  tension  of 
belts,  upon  which  are  partly  founded  the  formulae  employed  in  the 
calculation  of  the  experiments  upon  the  friction  of  journals  (or  axles). 

To  make  them,  I  placed  vertically  above  the  axle  of  the  water- 
wheel  and  of  the  pulley,  mounted  on  its  shaft,  a  cylindrical  oak 
drum,  with  a  diameter  of  Om,836,  and  whose  axis  was  about  3  metres 
from  that  of  the  wheel.  Around  this  drum,  d'  d',  and  of  the  pulley, 
d  d  (Fig.  69),  I  passed  a  belt ;  but,  instead  of  its  being  one  single 
piece,  it  was  in  two  parts  joined,  near  each  end,  by  one  of  the 
dynamometers  of  the  power  of  200  kilogrammes,  with  a  movable 
plate  and  style  which  are  described  in  Article  179.  These  dynamom- 
eters were  easily  placed  in  such  positions  that  that  of  the  descend- 
ing strip  was  near  the  upper  drum,  and  that  of  the  ascending  strip 
near  the  lower  drum,  in  such  a  manner  that  the  belt  could  move 
over  an  extent  of  nearly  2  metres  without  a  risk  of  the  dynamome- 
ters entangling  themselves  upon  the  drums. 

A  thread,  rolled  several  times  around  the  circumference  of  one  of 
the  grooves  of  the  plate  of  each  of  the  dynamometers,  and  fastened 
at  the  other  end  to  a  fixed  point,  compelled  this  plate  to  turn  when 
the  apparatus  was  in  motion ;  and,  if  the  displacement  was  only  iu 
proportion  to  the  extension  of  the  belt,  we  turned  the  plate  with  the 
hand  to  obtain  a  complete  trace  of  the  curve. 

This  trace  was  besides  obtained,  as  told  in  the  account  given,  by  a 
style  with  a  tube  and  capillary  orifice  incessantly  pressed  by  a  spring 
upon  the  sheet  of  paper  which  the  plate  carried. 

The  belt  being  passed  over  the  two  drums,  the  tension  of  the  strips 
of  the  belt  was  varied,  in  either  direction,  by  suspending  from  the 
exterior  circumference  of  the  upper  drum  a  plate, p,  which  we  loaded 
with  weights.  The  natural  or  primitive  tension  was  increased  by 
bringing  the  ends  of  the  belt  near  to  each  other,  or  by  shortening  it 
before  the  experiment. 


244  EXPERIMENTS    OF    A.   MORIN. 

Apparatus  for  Experiments  upon  the  Variation  of  Tension  of  Belts. 


r  t  rtrir  r  r  f 


U_l  \d 


Pig.  69. 


EXPERIMENTS    OF    A.   MOBIN.  245 

The  machinery  being  thus  prepared  for  taking  observations,  before 
loading  the  plate,  p,  we  traced  the  two  curves  or  circles  of  curvature 
of  each  of  the  dynamometers,  in  order  to  find  their  tension,  or  that 
of  the  belt  in  repose,  and  to  obtain  by  their  sum  the  double  of  the 
natural  tension.  One  can  understand,  besides,  that,  in  consequence 
of  the  movement  which  had  taken  place  in  one  way  or  another,  and 
which  had  necessarily  put  in  play  the  passive  resistances  of  the  forces, 
these  two  tensions  could  never  be  equal ;  but  this  is  of  little  conse- 
quence, since  we  only  want  their  sum.  This  done,  we  placed  upon 
the  plate  a  weight,  which,  being  suspended  from  the  circumference 
of  the  drum  by  a  cord  of  a  diameter  equal  to  the  thickness  of  the  belt, 
had  consequently  the  same  lever-arm  as  the  tensions.  The  strip  of  belt 
opposed  to  this  weight  tightened,  and  the  strip  placed  on  the  same  side 
relaxed,  and  we  traced  new  lines  of  curvature  of  the  dynamometers. 

One  could,  besides,  for  a  same  natural  tension,  make  a  different 
series  of  experiments,  including  the  motive  weights,  under  the  action 
of  which  the  belt  slipped  on  one  or  the  other  drum ;  and,  as  one  also 
had  the  opportunity  to  let  the  two  axles  turn  during  a  certain  time, 
under  the  action  of  the  developed  tensions,  one  can  see  that  the 
experiments  would  take  in  the  three  cases  in  practice,  namely :  that 
of  the  variation  of  tensions  before  the  movement  was  produced,  that  of 
this  variation  during  the  movement,  and  finally  that  of  the  slipping. 

It  is  not  necessary  to  add  that  each  one  of  the  dynamometers  had 
been  tested*  separately,  and  by  gradually  attaching  equal  weights  to 
them,  which  determined  the  curvature  whose  trace  we  had  preserved, 
we  had  obtained  an  exact  scale  of  loss,f  which  served  to  estimate  the 
corresponding  tension  at  each  curve  of  flexion  traced  in  the  experi- 
ments. 

These  preliminary  observations,  made  and  repeated  with  care, 
have  shown  that  one  of  the  dynamometers  increases  by  flexion 
Om,00292,  and  the  other  Om,00323,  for  each  kilogramme  of  increase  in 
the  weight  which  was  attached  to  it.  It  was  then  easy,  in  each  case, 
by  comparing  the  diameters  of  the  curves  of  flexion  obtained  with 

*  This  word,  in  the  original,  is  tare,  which  means  "spoiled,  injured,  ruined;" 
but  as  neither  of  these  would  answer  here,  I  have  substituted  "tested,"  as  com- 
ing nearer  the  technical  meaning.  The  word  tarer  is  "to  spoil,  to  injure,"  but 
means  also  to  bring  an  article  into  equilibrium  before  weighing  it;  hence  we 
may  decide  that  the  dynamometers  were  brought  into  equilibrium — were  regu- 
lated or  graduated  before  they  were  used. 

f  The  words  "  an  exact  scale  of  loss,"  by  good  authorities,  correspond  to  the 
original,  which  are  eschelle  de  tare  exacte,  and,  in  a  technical  sense,  may  be  strained 
to  mean  a  measure  of  the  error  by  which  to  make  proper  allowance  on  the  record. 


246  EXPERIMENTS    OF    A.    MORIN. 

the  scale  of  loss,  to  determine  the  tension  of  each  strip  of  the  belt 
with  sufficient  accuracy. 

Arrangement  of  Table  No.  III. 

174.  This  statement  shows  how  easy  these  experiments  were  by 
the  aid  of  this  apparatus,  and  there  remains  nothing  but  to  give  the 
results,  which  are  shown  in  the  following  table: 

The  1st  column  shows  the  numbers  of  the  order  of  experiment. 

The  2d  column  shows  the  weights  suspended  from  the  circum- 
ference of  the  drum,  including  that  of  the  plate. 

Deduced  from  the  com- 


The  3d  the  tension  of  the  strained  strip. 
The  4th  the  tension  of  the  slack  strip. 


parison  of  the  curve 
of    flexion    with    the 


scale  of  loss. 

The  5th  shows  the  sum  of  the  two  tensions,  or  the  double  of  the 
natural  tension. 

Observations  upon  the  Results  contained  in  the  Tables. 

175.  In  examining  the  results  contained  in  Table  III.,  we  see 
that  the  first  line  of  each  series  of  experiments  corresponds  to  the 
case  where  the  additional  weight  p  was  zero,  and  where  each  strip 
took  the  tension  corresponding  to  the  distance  of  the  axles  from  each 
other.  These  tensions  are  not  equal  on  account  of  the  inevitable 
action  of  passive  resistances  brought  into  play,  but  they  differ  very 
little  [from  each  other]  in  other  respects.  In  proportion  as  the 
Weight  suspended  from  the  drum  increases,  the  tension  of  one  of  the 
strips  increases,  and  that  of  the  other  diminishes,  but  in  such  a  man- 
ner that  their  sum  remains  constant,  as  the  fifth  column  of  the  table 
shows. 

These  results,  which  completely  confirm  the  theory  established  by 
M.  Poncelet,  besides  relating  to  tensions  whose  sum  rose  as  high  as 
90  kilogrammes  and  more,  the  highest  of  which  showed  as  high 
as  77  kilogrammes,  and  the  smallest  diminished  to  5  kilogrammes, 
comprise  nearly  all  cases  of  practice,  and  show  that  this  theory  can, 
with  surety,  be  applied  to  the  calculation  of  all  machines  driven  by 
belts. 

We  ought  then  to  regard  as  demonstrated,  both  by  theory  and 
practice,  that  in  the  transmission  of  motion  from  one  axle  to  another, 
by  the  aid  of  endless  belts,  that  the  sum  of  the  tensions  remains  con- 
stant, be  it  at  the  moment  of  passing  from  rest  to  motion,  or  during 
motion,  finally,  be  it  at  the  moment  when  the  belt  slips  upon  one  of 
the  drums. 


EXPERIMENTS    OF    A.    MOKIN. 


247 


176.     Table  No.  III. 

Experiments   upon  the  Variation  of  Tension  of  Endless   Belts  to  Trans- 
mit the  Motion  to  Axles  of  Rotation. 


INo.  OF 
EXPERIMENTS. 

WEIGHT 
SUSPENDED 
TO  CIRCUM- 
FERENCE 
OF  DRUM 

Q. 

TENSION 

SUM  OF 
TENSIONS. 

t  +  1'  =  2T. 

OBSERVATIONS. 

ASCENDING 

OR 

STRAINED 
STRIP. 

t. 

DESCEND- 
ING OR 
SLACK 
STRIP. 

t'. 

K. 

K. 

K. 

1 

o, 

17,49 

14,89 

32,38 

2 

20,23 

27,24 

5,82 

32,86 

[drum. 

3 

27,23 

28,63 

4,62 

33,25 

The  belt  slips  upon  the 

4 

o, 

39,41 

26,03 

55,44 

5 

10,23 

34,05 

21,23 

55,28 

6 

20,23 

38,82 

14,44 

55,26 

~)      The    dynamometers 

7 

30,23 

44,42 

10,96        55,38 

>-have  moved   about  a 

8 

44,23 

49,84 

9,41 

59,25 

j  meter. 

9 

0, 

33,43 

28,26 

61,69 

10 

25,23 

44,89 

18,83 

63,72 

Idem. 

11 

50,23 

53,40 

9,24 

62,64 

12 

o, 

30,34 

26,27 

56,71 

[drum. 

13 

52,00 

47,06 

7,19 

54,25 

The'  belt  slips  upon  the 

14 

o, 

48,76 

44,85 

93,61 

15 

25,23 

58,97 

31,86 

90,83 

16 

50,23 

71,20 

21,57 

92,77 

17 

o, 

44,69 

40,24 

84,93 

18 

50,23 

69,96 

18,49 

88,45 

19 

79,23 

77,39 

19,69 

97,05 

Idem. 

20 

o, 

39,32 

38,35 

77,67 

21 

40,23 

61,14 

20,03 

81,17* 

*  Besides  the  weight  Q  there  was  suspended  from  the  mean  circumference  of 
the  floats,  or  at  a  distance  of  lm,85  from  the  axis  of  the  wheel,  a  weight  of 
10k,229,  which  broke  the  equilibrium. 

NOTE. —  The  belt  employed  in  these  experiments  was  very  pliable,  soft,  and 
little  susceptible  to  polish  itself  by  slipping. 


248  EXPERIMENTS    OF    A.    MORIN. 

We  have  deduced  these  statements  from  experiments  Nos.  3,  13, 

and  19. 

f=  0,578,  f=  0,596,  f=  0,544, 

whose  mean  /=  0,589  exceeds  by  about  |  the  value  deduced  from 
direct  experiment  upon  the  new  belt  employed  in  the  experiments 
upon  the  friction  of  journals,  and  y^  of  that  which  was  deduced 
from  the  experiments  upon  a  very  rough  new  belt. 

Tension  that  can,  with  Security,  be  Applied  to  B&tts. 

177.  I  will  add  that  the  examination  of  the  condition  of  belts, 
after  these  experiments,  and  after  those  relating  to  their  slipping  on 
the  surface  of  the  drum,  has  shown  that  they  had  undergone  no 
apparent  change,  although  the  small  belt,  with  a  breadth  of  Om,028 
and  a  thickness  of  Om,005,  might  have  supported  a  strain  of  62  kilo- 
grammes, or  2k,25  per  square  millimetre  of  a  section,  and  that  the 
belt  employed  in  the  last  experiment,  which  was  very  old  and  very 
much  worn  on  the  edges,  with  a  breadth  of  Om,050  and  a  thickness 
of  Om,004,  was  for  some  time  subjected  to  a  strain  of  97  kilogrammes 
or  of  2k,06  per  square  millimetre.     We  see,  then,  that  in  practice 
belts  can  be  subjected  to  a  strain  calculated  at  the  rate  of  2  kilo- 
grammes per  square  millimetre*  of  their  section,  and  that  their  thick- 
ness being  besides  usually  limited  from  Om,004  to  Om,008  when  they 
are  no  longer  doubled,  one  can  determine  the  dimension  that  it  would 
be  proper  to  give  them,  and  beyond  which  there  would  be  no  advan- 
tage in  increasing  their  width  out  of  proportion,  as  is  sometimes  done. 

Experiments  upon  the  Variation  of  the  Tension  of  Endless  Cords 
or  Belts  used  in  Transmitting  Motion.  —  From  "  Morin's 
Mechanics,"  D.  Appleton  &  Co.,  N.  Y.,  I860. 

178.  "We  pass  now  to  an  experimental  proof  of  the  theory 
given  by  M.  Poncelet,  upon  the  transmission  of  motion  by  endless 
cords  or  belts,  and  will  first  give  a  description  of  its  nature. 

"  When  a  cord  or  belt  surrounds  two  pulleys  or  drums,  between 
which  it  is  designed  to  maintain  a  conjoint  motion,  care  is  taken  to 
give  it  a  sufficient  tension,  which  is  usually  determined  by  trial,  but 
which  it  would  be  best  to  calculate,  as  we  shall  see  hereafter.  The 
primitive  tension  is,  at  the  commencement,  the  same  for  both  parts 
of  the  belt,  and  this  equality,  established  in  repose,  is  only  destroyed 

*  The  practical  rule  given  by  Coulomb,  fixes  the  limit  of  the  strain  that  can, 
with  security,  be  given  to  a  thread  of  rope-yarn  at  40  kilogrammes,  which  comes 
very  near  to  3k,70  per  square  millimetre. 


EXPERIMENTS    OF    A.    MOBIN. 


249 


by  the  friction  of  the  axles,  which  may  act  in  either  direction,  accord- 
ing to  that  of  the  motion  of  the  pulleys.  Let  us  examine  how  this 
motion  is  transmitted  in  such  a  system.  Let  C  (Fig.  70)  be  the  motive 
drum  ;  C'  the  driven  drum  ;  T!  the  primitive  tension  common  to  the 
parts  A  A'  and  B  B'  of  the  belt,  from  the 
moment  when  the  drum  C  begins  to  turn 
until  it  commences  to  turn  the  drum  C'. 

"  The  point  A  of  primitive  contact  of  the 
part  A  A'  advances,  in  separating  from  the 
point  A',  in  the  direction  of  the  arrow  ;  the 
strip  A  A'  is  stretched,  and  its  tension  in- 
creased by  a  quantity  proportional  to  this 
elongation,  according  to  a  general  law  proved 
by  experiment  upon  traction.  At  the  same 
time  the  point  B  of  contact  of  the  part  B  B' 
approaches,  by  the  same  quantity,  towards 
the  point  B',  so  that  the  portion  B  B'  is  di- 
minished by  a  quantity  equal  to  the  increase 

of  that  of  A  A'.  If,  then,  we  call  T  the  tension  of  the  driving  por- 
tion, A  A',  at  the  instant  of  its  being  put  in  motion;  T'  the  tension 
of  the  driven  part,  B  B'  ;  t  the  quantity  by  which  the  primitive  ten- 
sion, Tz  is  increased  in  the  portion  A  A',  and  diminished  in  the  part 
B  B',  we  shall  have 


and,  consequently, 


Fig,  70. 


T+  Tf  =  i2 


"Then,  at  any  instant,  the  sum  of  the  two  tensions,  T  and  T,  is 
constant,  and  double  the  primitive  tension. 

"  Now,  it  is  evident  that,  in  respect  to  the  driven  drum,  C',  the 
motive  power  is  the  tension,  T,  and  that  the  tension,  T'r  acts  as  a 
resistance  with  the  same  lever  arm,  so  that  the  motion  is  only  pro- 
duced and  maintained  by  the  excess,  T  —  1",  of  the  first  over  the 
second  of  these  tensions. 

"  If  the  machine  is,  for  example,  designed  to  raise  a  weight,  Q, 
acting  at  the  circumference  of  an  axle  with  a  radius,  B/,  it  is  easy 
to  see,  according  to  the  theory  of  moments,  that,  at  any  instant  of  a 
uniform  motion  of  the  machine,  we  must  have  the  relation 


being  the  pressure  upon  the  journals  and  r  their  radius. 


250  EXPERIMENTS    OF    A.    MORIN. 

"  The  pressure  is  easily  determined  ;  for,  calling  a  the  angle  formed 
by  the  directions  A  A'  and  B  B'  of  the  belts  with  the  line  of  the 
centres,  C  C',  M  the  weight  of  the  drum,  we  see  immediately  that 


=  V\M  +  Q  +  (T—  T'}  sin.  aj  +  (T+  T')  cos.9  a, 

an  expression  which,  according  to  the  algebraic  theorem  of  M.  Pon- 
celet  cited  in  No.  227,*  has  for  its  value  to  2V  nearly  ;  when  the  first 
term  under  the  radical  is  greater  than  the  second, 


N=  0.96  [M  +  Q  +  (T—  T')  gin.  ci]  +  04(T+  T')  cos.  a. 

"This  value  of  N  being  introduced  into  the  formula  for  equality 
of  moments,  we  have  a  relation  containing  only  the  values  of  the 
resistance,  Q,  and  of  the  tensions.  But  as  it  may  be  somewhat  com- 
plicated for  application  —  observing  that  in  most  cases  the  influence  of 
the  tensions  T  and  T'  upon  the  frictions  will  be  so  small  that  it  may 
be  neglected,  at  least  in  a  first  approximation  —  we  proceed  as  follows  : 

"  First,  neglecting  the  influence  of  the  tensions  upon  the  friction, 
we  have  simply,  in  the  actual  case, 


N=M+  Q, 
and,  consequently, 

(T-  T')R=Q  Rf  +/(Jf  +  §)  r; 
whence  we  deduce 


which  furnishes  a  first  value  for  the  difference  of  tensions,  which  is 
the  motive  power  of  the  apparatus. 

"  But  this  is  not  sufficient  to  make  known  these  tensions,  and  it  is 
necessary  to  determine  the  primitive  tension,  T',  so  that  in  no  case 
the  belt  may  slip. 

"  According  to  the  theory  of  M.  Prony,  we  have,  at  the  instant  of 
slipping,  between  the  tension  T  and  T',  the  relation 

T=  T  x  2,718  +fj^T'  =  K  F, 

the  number  K  being  the  quantity  depending  upon  the  nature  and  con- 
dition of  the  surfaces  of  contact  as  well  as  upon  the  angle  —  embraced 
by  the  belts  upon  the  drum,  C'.  These  quantities  are  known,  and 

*  See  "Morin's  Mechanics,"  p.  266,  D.  Appleton  &  Co.,  1860. 


EXPERIMENTS    OF    A.    MORIN.  251 

we  may  in  each  case  calculate  the  value  of  K  by  this  formula,  or 
take  it  from  the  table  on  p.  122,  which  answers  to  nearly  all  the 
cases  in  practice. 

"  By  means  of  this  table  we  have,  then,  the  value  of  T  =  KT',  and 
consequently 

T—  T'=(K—1)  T'=Q, 

Q  representing  the  greatest  value  which  the  difference  of  tensions 
should  attain,  to  overcome  the  useful  and  passive  resistances. 

"  From  this  relation  we  may  derive  the  smallest  tension  to  be 
allowed  to  the  driven  portion  of  the  belt,  to  prevent  its  slipping. 

"  We  thus  have 

T_     Q 

~ 


"  We  should  increase  this  value  by  TV  at  least,  to  free  it  from  all 
hazard  of  accidental  circumstances,  and  to  restore  the  account  of  the 
influence  of  the  tensions  upon  the  friction,  which  was  neglected. 

"  This  established,  we  have 


and  consequently 


= 

2  2K—1 


"  All  the  circumstances  of  the  transmission  of  motion  will  then  be 
determined. 

"If  these  first  values  of  T,  T'  and  Tx  are  not  considered  as  suffi- 
ciently correct,  we  may  obtain  a  nearer  approximation  by  introducing 
them  in  the  value  of  the  pressure  N,  and  thus  deduce  a  more  exact 
value  of  Q,  which  will  serve  to  calculate  anew  T',  then  T  and  T!." 

Dynamometer  Attachments. 

179.  "Around  this  drum  and  the  pulley  was  passed  a  belt,  which, 
instead  of  being  in  one  piece,  was  in  two  parts,  joined  at  each  end  by 
a  dynamometer  with  a  plate  and  style,  of  a  force  of  441  Ibs.  More- 
over, these  dynamometers  were  easily  secured  in  positions,  such,  that 
that  of  the  descending  portion  of  the  belt  was  near  the  upper  drum, 
and  that  of  the  ascending  near  the  lower  drum.  Thus  the  belt 
could  be  moved  over  a  space  of  6,56  feet  without  the  risk  of  the 
instruments  being  involved  with  the  drums. 

"A  thread,  wound  several  times  around  the  circumference  of  one  of 


252  EXPERIMENTS    OF    A.    MORIN. 

the  grooves  of  the  plate  of  each  of  the  dynamometers,  and  attached 
by  the  other  end  to  a  fixed  point,  caused  the  plate  to  turn  when  the 
apparatus  was  in  motion,  and  the  paper  with  which  the  plate  was 
covered  received  thus  the  trace  of  the  style  of  the  dynamometer. 

"The  belt  being  passed  over  the  two  drums,  the  tensions  of  the  parts 
were  varied  at  will,  in  either  direction,  by  suspending  at  the  circum- 
ference of  the  upper  drum  a  plate,  p,  charged  with  weights.  As  to 
the  primitive  tension,  it  was  increased  by  bringing  nearer  together 
the  ends  of  the  belt,  or  in  diminishing  its  length  before  the  experi- 
ment. 

"  The  apparatus  being  thus  prepared  for  observations  before  loading 
the  plate,  p,  we  traced  the  circles  of  flexion  of  each  of  the  dyna- 
mometers, so  as  to  have  the  tensions  of  the  belt  at  rest,  and  to  obtain 
by  their  sum  the  double  of  the  primitive  tension,  Tx.  We  may  con- 
ceive that  these  two  tensions  can  never  be  quite  equal ;  but  that  is  not 
important,  inasmuch  as  we  have  to  deal  only  with  their  sum. 

"  This  obtained,  we  load  the  plate  with  a  weight  which,  being  sus- 
pended upon  the  circumference  by  a  cord  of  a  diameter  equal  to  the 
thickness  of  the  belt,  has  the  same  lever-arm  as  the  tensions.  That 
part  of  the  belt  opposed  to  this  weight  is  stretched,  and  the  part  on 
the  same  side  is  slackened,  and  we  trace  the  new  curves  of  the  flexion 
of  the  dynamometers. 

"  For  this  same  primitive  tension  we  may  make  a  series  of  experi- 
ments up  to  the  motive  weight,  under  the  action  of  which  the  belt 
slides  upon  either  drum." 


CHAPTER   VIII. 

ROPE  TRANSMISSION. 

The  Transmission  of  Power  by  Wipe  Ropes,  by  W.  A.  Roebling, 
C.  E.,  Trenton,  N.  J. 

180.  "  The  use  of  a  round  endless  mire  rope  running  at  a  great 
velocity  in  a  grooved  sheave,  in  place  of  a  flat  belt  running  on  a  flat- 
faced  pulley,  constitutes  the  transmission  of  power  by  wire  ropes. 

"  The  distance  to  which  this  can  be  applied  ranges  from  50  or  60 
feet  up  to  about  3  miles.  It  commences  at  the  point  where  a  belt 
becomes  too  long  to  be  used  profitably,  and  can  thence  be  extended 
almost  indefinitely. 

"  In  point  of  economy  it  costs  only  ^  of  an  equivalent  amount  of 
belting,  and  the  ^  of  shafting.  .  .  . 

"  The  range  in  the  size  of  wire  ropes  is  small,  varying  only  from 
|  to  |  inch  diameter  in  a  range  of  3  to  250  horse-power. 

"  In  regard  to  cost,  the  ropes  are  the  cheapest  part  of  a  transmis- 
sion. For  instance,  a  No.  22  rope  —  conveying,  say  25  horse-power 
—  costs  8  cents  per  foot,  whereas  an  equivalent  belt  costs  about  $1.40 
per  foot.  .  .  .  Their  duration  is  from  2^  to  5  years,  according 
to  the  speed. 

"  For  the  smaller  powers  it  is  advisable  to  take  a  size  larger,  for 
the  sake  of  getting  wear  out  of  the  rope ;  although  it  must  be  borne 
in  mind  that  a  larger  rope  is  always  stiffer  than  a  small  one,  and 
therefore  additional  power  is  lost  in  bending  it  around  the  sheave. 
An  illustration  of  that  is  seen  in  the  case  of  the  14-feet  wheel  in 
the  table  (page  255),  where  a  f  rope  gives  less  power  than  a  f  rope, 
simply  because  it  is  so  much  stiffer. 

"  Ropes  for  this  purpose  are  always  made  with  a  hemp  core,  to 
increase  their  pliability. 

"  It  is  often  required  to  convey  the  entire  power  of  a  certain  shaft 
which  is  driven  by  a  belt  of  a  given  size.  In  such  a  case  a  simple 
rule,  agreeing  with  the  average  result  of  practice,  is,  that  70  square 
feet  of  belt  surface  are  equal  to  one  horse-power. 

253 


254  HOPE    TRANSMISSION. 

"  Take,  for  example,  a  belt  one  foot  wide  running  at  the  rate  of 

1400'+!' 
1400  Fpm  ;  then  the  horse-power  = —  =  20 ;  and  by  referring 

to  the  table  we  find  the  diameter  of  the  wheel  corresponding  to  this 
horse-power,  and  making  the  same  number  of  revolutions  that  the 
belt-pulley  does. 

Distance  of  Transmission. 

"  The  wire  rope  transmission  table  is  arranged  for  distances  ranging 
from  80  up  to  350  or  400  feet  in  one  stretch.  For  a  single  stretch 
extended  to,  say  450  feet,  where  no  opportunity  is  presented  for  put- 
ting in  an  intermediate  station,  we  must  use  a  rope  one  size  heavier ; 
and  in  a  case  where  there  is  not  sufficient  head-room  to  allow  the  rope 
its  proper  sag,  and  it  has  to  be  stretched  tighter  in  consequence,  we 
must  also  take  a  rope  one  size  heavier. 

Short  Transmission. 

"  Whenever  the  distance  is  less  than  80  feet,  the  rope  has  to  be 
stretched  very  tight,  and  we  no  longer  depend  upon  the  sag  to  give  it 
the  requisite  amount  of  tension.  Here  we  must  take  a  rope  two  sizes 
heavier  than  is  given  in  the  table,  and  run  at  the  maximum  speed 
indicated.  It  is  also  preferable  to  substitute  in  place  of  the  rope 
of  49  wires  a  fine  rope  of  133  wires  of  the  same  diameter,  which  pos- 
sesses double  the  flexibility,  runs  smoother,  and  lasts  longer.  In 
fact,  the  substitution  of  a  fine  rope  for  a  coarse  one  can  be  done  with 
advantage  in  every  case  in  the  table  where  the  size  admits  of  it. 

Splices. 

"  Both  kinds  of  rope  are  spliced  with  equal  facility.  The  splices 
are  all  of  the  kind  known  as  the  long-splice ;  the  rope  is  not  weak- 
ened thereby,  neither  is  its  size  increased  any,  and  only  a  well-prac- 
tised eye  can  detect  the  locality  of  one. 

Relative  Height  of  Wheels. 

"  It  is  not  necessary  that  the  two  wheels  should  be  at  the  same 
level,  one  may  be  higher  or  lower  than  the  other  without  detriment ; 
and  unless  this  change  of  level  is  carried  to  excess,  there  need  be  no 
change  in  the  size  of  wheel  or  speed  of  rope :  the  rope  may  have  to 
be  strained  a  little  tighter.  As  the  inclination  from  one  wheel  to 
another  approaches  an  angle  of  45°,  a  different  arrangement  must 
be  made,  as  will  be  shown  hereafter. 


Table  of 


ROPE    TRANSMISSION. 
Transmission  of  Power  by  Wire  Ropes. 


255 


H 

II 

III 

s*a 
fi°£ 

HORSE- 
POWER. 

DIAM. 

OF 

WHEEL. 

II 

HI 

a»i 

HORSE- 
POWER. 

Feet. 

4 

80 

23 

1 

3.3 

Feet. 

9 

140 

20 
19 

u 

70. 
72.6 

4 

100 

23 

1 

4.1 

10 

80 

19 

5     11 

55. 

o 

U\7 

18 

S    T6" 

58.4 

4 

120 

23 

3 

B 

5. 

10 

100 

19 
18 

1     11 

68.7 
73. 

4 

140 

23 

1 

5.8 

10 

120 

19 

18 

6        J-l 

82.5 
87.6 

5 

80 

22 

A 

6.9 

10 

140 

19 
18 

96.2 
102.2 

5 
5 
5 
6 
6 

100 
120 
140 
80 
100 

22 
22 
22 
21 
21 

7 
75 

A 

15 

ii 

8.6 
10.3 
12.1 
10.7 
13.4 

11 
11 
11 
11 

80 
100 
120 
140 

18 
19 
18 
19 
18 
19 
18 

1*1 

1  H 

64.9 
75.5 
81.1 
94.4 
97.3 
113.3 
113.6 
132.1 

6 

120 

21 

o  J, 

if 

16.1 

12 

80 

18 
17 

Ul 

93.4 
99.3 

6 

140 

21 

0  £ 

18.7 

12 

100 

18 
17 

Hi 

116.7 
124.1 

7 

80 

20 

\ 

16.9 

12 

120 

18 
17 

Hi 

140.1 
148.9 

7 

100 

20 

J 

21.1 

12 

140 

18 
17 

11  1 

163.5 
173.7 

7 

120 

20 

i 

25.3 

13 

80 

18 
17 

HI 

112. 
122.6 

7 

140 

20 

i 

29.6 

13 

100 

18 
17 

HI 

140. 
153.2 

8 

80 

19 

t 

22. 

13 

120 

18 
17 

11  1 

168. 
183.9 

8 

100 

19 

1 

27.5 

14 

80 

17 
16 

1  1 

148. 
141. 

8 

120 

19 

1 

33. 

14 

100 

17 
16 

1  1 

185. 
176. 

8 

140 

19 

1 

38.5 

14 

120 

17 
16 

1  1 

222. 
211. 

9 

80 

20 
19 

i  1 

40. 
41.5 

15 

80 

17 
16 

1  i 

217. 
217. 

9 

100 

20 
19 

1     5 
2    T 

50. 
51.9 

15 

100 

17 

16 

1  1 

259. 
259. 

9 

120 

20 
19 

M 

60.     - 
62.2 

15 

120 

17 
16 

1  I 

300. 
300. 

256  ROPE    TRANSMISSION. 

Deflection  or  Sag  of  the  Ropes. 

"  In  the  following  illustration  the  upper  rope  is  the  pulling  rope 
and  the  lower  one  the  loose  following  rope.  When  the  rope  is  work- 
ing, the  tension,  T,  in  the  upper  rope,  is  just  double  that  in  the  lower 
rope,  hence  the  latter  will  sag  much  lower  below  a  horizontal  line 
than  the  upper  one. 

"  When  the  rope  is  at  rest,  both  ropes  will  occupy  the  position 
indicated  by  the  dotted  line,  and  will  have  a  uniform  tension. 

"  The  best  way  in  practice  is  to  hang  up  a  wire  in  the  position  the 
rope  is  to  occupy  at  rest ;  that  has  to  be  done  in  any  case,  in  order 


Fig.  71. 

to  get  the  length  of  rope  needed.  Then  hang  it  so  that  the  deflec- 
tion, D',  below  the  horizontal  line,  is  about  ^  of  the  whole  distance 
from  wheel  to  wheel.  The  deflection,  D,  of  the  upper  running  rope 
will  then  be  about  ^  to  -^. 

"  The  deflection,  D",  of  the  lower  working  rope  is  on  an  average 
one-half  greater  than  the  deflection  D'  of  the  rope  at  rest.  This  is 
of  importance,  as  we  should  know  beforehand  whether  the  lower  rope 
is  going  to  scrape  on  the  ground  or  touch  other  obstructions ;  in  that 
case  we  either  have  to  dig  a  trench  for  the  lower  rope  to  run  in,  or 
else  raise  both  wheels  high  enough  to  clear. 

"  Practically,  however,  it  is  not  necessary  to  be  so  particular  about 
this  matter,  on  account  of  the  stretch  in  the  rope.  Wire-rope 
stretches,  comparatively,  very  little ;  still,  there  is  some  stretch, 
and  it  is  well  to  allow  for  it  by  stretching  the  rope  a  little  too  tight 
at  first.  After  running  a  little  it  will  hang  all  right.  When  the 
rope  is  very  long,  it  is  advisable  to  take  up  the  stretch  at  the  end 
of  two  or  three  months,  as  a  slack  rope  does  not  run  so  steadily  as  a 
tight  one. 

"  Whenever  the  direction  of  the  motion  of  the  driving  wheel  is 
not  fixed  by  other  circumstances,  it  is  often  advisable  to  make  the 


ROPE    TRANSMISSION.  257 

lower  rope  the  pulling  rope,  and  the  upper  the  follower,  as  here 
shown.     In  this  way  obstructions  can  be  avoided,  which,  by  the 


Fig.  72. 

other  plan,  would  have  to  be  removed.  The  ropes  will  not  interfere 
as  long  as  the  difference  between  the  two  deflections,  D'  and  D",  is 
less  than  the  diameter  of  the  wheel. 

"  These  limits  are  of  use  whenever,  on  account  of  rocks  or  other- 
wise, we  have  to  move  the  wheels  closer  together,  and  the  question  is 
how  far  to  have  them  apart  with  a  certain  deflection. 

The  Wheels. 

"  The  bottom  of  the  groove  in  the  wheels  is  made  a  little  wider,  to 
prevent  the  filling  from  flying  out.  The  rope  should  always  run 
on  a  cushion  of  some  kind,  and  not  on  the  iron,  which  quickly  wears 
it  out. 

"  A  variety  of  material  is  used  for  this  filling  —  soft  wood,  India- 
rubber,  leather,  old  rope  tarred,  and  oakum. 

"To  use  end-wood  the  rim  has  to  be  constructed  on  a  different 
plan  from  that  shown  here.  The  objections  to  it  are  that  it  is  liable 
to  shrink,  and  crack  and  fly  out;  it  is  also  more  severe  on  the 
rope.  India-rubber  is  a  very  good  material ;  strips  of  an  inch 
square  or  less  can  be  wedged  in  very  quickly,  and  will  last  a  long 
time ;  the  price,  however,  is  50  to  60  cents  per  pound,  which  is 
rather  against  it. 

"  My  own  practice  has  been  to  use  leather,  also  rope  and  oakum. 
The  leather  is  cut  in  sections  of  the  shape  shown  in  Fig.  73,  and  set 
in  on  end  around  the  rim ;  scraps  can  be  used,  cut  from  old  shoes, 
pieces  of  leather  belting,  etc. ;  they  are  very  thin,  and  it  takes  at  least  a 
thousand  for  a  7-feet  wheel.  When  many  are  wanted,  it  is  worth  while 
to  make  a  die,  to  cut  them  out  fast.  This  is  the  most  durable  filling 
that  can  be  made. 
17 


258 


ROPE    TRANSMISSION. 


"  Again,  by  wedging  the  groove  full  of  tarred  oakum  a  filling  is 
also  obtained,  nearly  as  good  as  leather,  costing  less,  and  not  so 

tedious  to  put  in.  Another 
plan,  which  I  have  tried  with 
success,  is  to  revolve,  the  wheels 
slowly,  and  let  a  lot  of  small- 
sized  tarred  ratlin,  or  jute- 
yarns,  wind  up  on  themselves 
in  the  groove  ;  then  secure  the 
end,  and,  after  a  day  or  two  of 
running,  the  pressure  of  the 
rope,  together  with  the  tar, 
will  have  made  the  filling 
compact.  This  makes  a  cheap 
filling. 

"  The  double-grooved  wheels 
are  filled  in  the  same  way. 

"  The  rope  will  run  on  such 
filling  without  making  any 
noise  whatever,  and  soon  wears 
in  a  round  groove  for  itself. 

"  A  section  of  the  rim  of  a 
6-feet  wheel  is  here  shown  with 
the  dimensions  marked. 

"  The  diameter  of  the  wheel 
is  not  reckoned  from  the  out- 
side of  the  rim,  but  from  the 
top  of  the  filling,  which  corre- 
sponds to  the  circle  described 
by  the  rope.  The  hub  is  made  of  ample  size,  so  as  to  admit  of  being 
bored  out  for  shafts,  ranging  from  2  to  3?  inches. 

.  .  .  "  The  rope,  while  running,  requires  no  protection  from  the 
weather.  If  it  has  to  stand  still  much,  pour  some  hot  coal-tar  from 
a  can  on  the  rope  in  the  groove  of  the  wheel  while  running. 

'*  Whenever  there  is  no  room  for  the  sag  of  the  rope,  and  it  is  incon- 
venient to  raise  the  wheels  higher,  or  a  ditch  cannot  be  dug,  it  may 
be  supported  by  a  roller  in  the  middle.  This  supporting  roller  must 
be  in  the  centre  of  the  span,  and  must  be  at  least  half  the  size  of  the 
larger  wheels."  .  .  . 

"Transmissions  are  in  operation  a  mile  in  length.  The  loss  of 
power  from  friction,  etc.,  or  bending  of  rope,  does  not  amount  to  10 


73, 


ROPE    TRANSMISSION. 


259 


per  cent,  per  mile,  and  need  not  be  taken  into  account  at  all  for  only 
one  station.  No  slipping  of  the  rope  in  the  groove  ever  occurs  with 
a  proper  filling. 

"  With  bearings  of  a  sufficient  length  under  the  shaft  of  the  centre 
wheel,  and,  by  providing  them  with  a  self-feeding  oil-cup,  the  axle 
friction  is  reduced  to  a  minimum.  .  .  ." 

We  insert  here  the  general  wire-rope  table  in  full,  to  which  refer- 
ence is  made  in  the  preceding  notes. 

Table  of  Wire  Rope,  Manufactured  by  J.  A.  Roebling's  Sons,  Trenton,  N.  J. 


EOPE  OP  133  WlKES. 

EOPE  OF  49  WIRES. 

1 
I 

a 

a 

of  Hemp 
ivalent 
Inches. 

| 

| 

d 

0. 

80s 

"11 

1 

3 

1 

s| 

'o 

|{J 

1 

1 

"5 

•    Q2        & 

1 

1 
1 

jl 

III 

i 

1 

ii 

P 

111 

EH' 

S 

S 

P 

g«0> 

H 

6 

p 

8 

1 

6| 

ju 

74  00 

15i 

11 

4| 

36  00 

10| 

2 

64 

24 

65  00 

12 

4| 

30  00 

io4 

3 

51 

1| 

54  00 

132 

13 

3| 

25  00 

9^ 

4 

5 

43  60 

12 

14 

31 

20  00 

8-j 

5 

*f 

li 

35  00 

10  3 

15 

3 

16  00 

71 

6 

4 

1? 

27  20 

9| 

16 

2| 

12  30 

6: 

7 

B| 

l-i 

20  20 

8 

17 

2| 

8  80 

5i 

8 

s| 

1 

16  00 

7 

18 

2^ 

7  60 

5~ 

9 

2| 

11  40 

6 

19 

1-j 

5  80 

4-1 

10 

21 

8  64 

5 

20 

1-| 

4  09 

4 

10] 

24 

5  13 

4J 

21 

1| 

2  83 

3| 

!f 

4  27 

4 

22 

11 

2  13 

10  3 

li 

i 

3  48 

3| 

23 

H 

1  65 

2^ 

24 

i 

1  38 

24 

25 

i. 

1  03 

2 

Ropes  from  No.  8  to  No.  10|  are 

26 

1 

0  81 

1| 

specially  adapted  for  hoisting-rope. 

27 

1 

0  56 

*I 

Copper   and    steel    ropes    corre- 

m 

sponding   to   the    above    sizes   are 
also  made. 

28 
29 



Large  Sash  Cord. 
Small          " 

"  When  the  power  is  to  be  conveyed  nearly  vertically,  no  good 
result  is  obtained  by  running  the  rope,  say  from  A  to  B,  direct, 


260  ROPE    TRANSMISSION. 

as  indicated  by  dotted  lines   in  the   figure   below,  since  it  would 

slip. 

"  Two  carrying  sheaves,  G  and  D,  must  be  put  up  vertically  above 
A,  giving  a  horizontal  stretch  from  C  and  D  to  B. 
This  is  necessary,  in  order  to  maintain  the  required 
tension  in  the  rope,  which  can  be  obtained  in  no 
other  way.  A,  B,  and  C,  and  even  D,  should  be  of 
the  same  size ;  yet  D,  which  supports  the  following 
rope,  may  be  made  smaller  without  damage. 

"This  arrangement  must  be  borne  in  mind 
whenever  the  source  of  power  is  located  in  the 
cellar,  and  we  want  to  carry  it  to  an  upper  story 

and  distribute  it  horizontally." 

Transmission  of  Motive  Forces  to  a  Great  Distance. 

By  A.  Achard,  C.  E.,  of  Geneva,  Switzerland. 

Published  by  Dunbd,  Paris,  1876. 

Translated  by  J.  WM.  HUTTINGER,  Member  of  the  Franklin  Institute,  Philada. 

181*  The  transmission  by  cables  is  only  an  extension  of  the 
transmission  by  belts  which  are  universally  employed  in  the  interior 
of  shops.  Before  touching  upon  the  peculiar  properties  of  cables,  it 
is  proper  to  mention  what  may  be  said  in  general  about  funicular 
transmission. 

Funicular  transmission  consists  of  2  shafts,  one  of  which  is  required 
to  transmit  to  the  other  its  rotary  movement,  by  2  mounted  pulleys, 
one  on  one  shaft,  the  other  on  the  other,  lastly,  the  funicular  organ, 
either  an  endless  belt  or  an  endless  cable,  which  we  will  call  cord,  for 
the  sake  of  brevity,  without  prejudging  its  nature.  We  will  look 
only  at  the  case  where  the  2  shafts  are  parallel,  and  where  the  mean 
plan  of  the  2  pulleys  coincides,  for,  as  we  shall  see  further  on,  this 
is  the  only  thing  which  interests  us  on  the  subject  of  cables. 

At  any  instant  whatever,  one  can  conceive  the  cord  as  divided  into 
4  parts :  the  length  applied  to  the  conducting  pulley,  the  length 
applied  to  the  conducted  pulley,  lastly,  the  2  lengths  free.  The 
latter  are  called  the  strips  of  the  cord. 

The  active  organ  of  transmission  is  the  strip  which  enrolls  itself 
upon  the  conducting  pulley,  and  unrolls  itself  from  the  pulley  moved, 
in  other  words,  which  receives  from  the  first  a  traction  which  it  trans- 
mits to  the  second.  For  this  reason  it  is  called  the  conducting  strip ; 
for  the  same  reason  the  other  is  called  the  conducted  strip. 


ROPE    TRANSMISSION. 


261 


Being  thus,  let  A,  Fig.  75,  be  the  motor  shaft,  with  its  pulley  of  a 
radius  R,  and  B  the 
shaft  moved  with  its 
pulley  of  a  radius  R'. 
A  power  P  acts  upon 
the  first  tangentially  to 
a  circle  of  a  radius  rt 
and  a  resistance  Q  acts 
upon  the  second  tan- 
gentially to  a  circle  of 
a  radius/.  The  arrows, 
which  give  the  idea  of 


rotation,  show  that  it  is 

the  upper  cord  that  is  the  conductor  or  motor. 

In  order  that  transmission  may  take  place,  it  is  necessary  that  the 
pulley,  A,  draw  the  cord,  and  that  the  latter,  in  its  turn,  draw  the 
pulley,  B.  This  cannot  take  place  but  by  reason  of  the  adherence 
of  the  cord  to  the  felly,  or  rim,  of  the  pulleys,  and  this  adherence 
depends  upon  2  elements  —  the  roughness  of  the  parts  in  contact  and 
the  tension  of  the  cord. 

Call  T  the  tension  of  the  conducting  strip,  and  t  that  of  the  con- 
ducted strip.  We  can  imagine  the  2  strips  cut,  and  the  tension 
replaced  by  tractions,  respectively  equal  to  T  and  to  t,  and  acting  in 
regard  to  each  pulley  as  the  tensions  do.  In  this  way  the  conditions 
of  uniform  movement  can  be  regarded  separately  for  each  pulley. 
They  are,  first  throwing  aside  passive  resistances  : 

For  the.  conducting  pulley,  regarding  t  as  acting  in  comparison  as 
power,  and  T  as  resistance  : 


from  which  T  —  t  =  P^  > 


(1) 


For  the  pulley  moved,  observing  that  in  respect  to  the  latter,  that 
T  is  the  power,  while  t  acts  as  the  resistance: 


TRf  —  tR—  Qr'  =  o, 


whence  T  —  t  = 


(2) 


T  T 

The  equations  (1)  and  (2)  show  that  the  quantities  P^  and  Qjp, 
necessarily  equal  between  themselves,  omitting  passive  resistances,  are 


262  ROPE    TRANSMISSION. 

besides  equal  to  T  —  t.  But  this  is  not  sufficient  to  determine  T  and 
t ;  the  condition  of  adherence  will  supply  this. 

For  which  let  the  force,  P,  cause  the  pulley,  A,  to  slip  under  the 
cord  without  moving  the  latter,  it  will  be  necessary  that  this  force 

agree  with  the  surface  of  the  pulley,  that  is  to  say  P— »  let  it  be  at 

least  equal  to  the  friction  which  there  may  be  between  the  cord  and 
the  surface  of  the  pulley,  if  this  slipping  had  taken  place.  This  fric- 
tion has  for  its  measure  the  minimum  error  which  ought  to  exist 
between  the  tension  T  and  t  of  the  2  strips,  for  which  the  strip  of 
tension  T  draws  the  other  by  slipping  upon  the  immovable  pulley  ; 
for  the  friction  depends  only  upon  the  relative  movement,  which  is 
the  same  in  the  two  cases.  We  know,  by  a  known  theory,  that  this 

T 

error  ought  to  be  such  that  we  can  have  ,  =  ef*  (e  =  the  base  of  the 

natural  logarithms, /=  the  coefficient  of  friction  relative  to  the  two 
substances  in  contact,  a  =  the  value,  ascribed  to  the  radius  of  the  arc 
of  the  pulley  embraced  by  the  cord).  From  this  equation  one  can 
deduce  the  error  T  —  t  in  function,  be  it  of  t  or  of  T  at  will.  By 
taking  t,  we  find  T  —  t  =  t  (e/a —  1).  Consequently,  t  being  provi- 
sionally indetermined,  we  will  find  that  the  pulley,  A,  will  draw  the 

cord  if  P^<*  (e>—  1),  and  will  not  draw  it  if  f~>t  (ef*  —  l). 
K  K 

The  same  holds  good  as  far  as  it  concerns  the  pulley  moved,  the 
/  / 

cord  will  draw  it  if  Q™<2  (e&  —  1),  and  will  not  draw  it  if  Qo>>< 
xv  xv 

(eft  —  1),  (j8  being  the  arc  embraced  upon  this  pulley,  and  /  can  take 
another  value,  according  to  the  nature  of  the  pulley).  It  is  required 
then,  in  order  that  the  strictly  necessary  value  of  t  be  obtained,  that 

r  r' 

the  quantity  P^,  or  its  equal  QTT-,  be  equal  to  the  smaller  of  the 

XV  XV 

two  quantities  t  (efa  —  1)  and  t  (efi —  1).     This  value  is  obtained 

r  r' 

then,  by  dividing  P—  or  Q^,  by  the  smaller  of  the  two  quantities 

(e/a  —  1)  and  (e&  —  1).  Having  once  determined  t,  T  is  immediately 
deduced  from  it,  since  T  —  £  is  given  by  (1)  and  (2). 

Algebraically  speaking,  the  solution  of  the  problem  comes  back 
to  one  of  the  equations  (1),  and  (2)  the  other  equation, 

T 

7=*,  (3) 

or  k  is  the  smaller  of  the  two  quantities  eSa  and  e&. 


ROPE    TRANSMISSION.  263 

It  is  easy  to  take  account  as  proof  a  posteriori  of  the  preceding 
reasoning,  that  the  tensions  determined  by  this,  which  requires  the 
pulley  of  least  adherence  will  be,  for  the  strongest  reason,  sufficient 
for  the  pulley  of  greatest  adherence,  whatever  may  be  that  of  the  two 
which  is  conductor  and  which  is  conducted. 

In  practice,  in  view  of  the  irregularities  of  the  power  to  be  trans- 
mitted, it  is  advisable  to  increase  the  tensions ;  and  in  order  to  keep 
account  of  this  necessity,  we  must  give  to  Tc  a  co-efficient  n,  which  is 
<  1,  and  which  is  as  much  less  as  the  irregularities  are  great.  We 
will  replace,  then,  the  equation  (3)  by 

-=**&  (3a.) 

After  having  thrown  passive  resistances  out  of  account  to  simplify 
the  reasonings,  it  is  necessary  to  bring  them  into  the  question.  They 
are  2  in  number,  one  of  which  comes  in  whatever  may  be  the  mode 
of  communicating  the  movement  from  one  shaft  to  another,  while  the 
second  is  peculiar  to  the  funicular  organ.  The  first  consists  in  the 
friction  of  the  bearings.  Each  shaft  is  sustained  by  two  supports  or 
rests,  holding  the  bearings  which  guide  its  movement  of  rotation.  If 
we  call  /'  the  coefficient  of  friction,  in  reference  to  this  contact,  the 

f 

friction  of  a  support  will  be  the  product  of    .     *_    ,2,  by  the  pressure 

f 

which  the  shaft  exercises  upon  it.     The  quantity  ^     ^     2,  which  we 

design  to  abridge  by  f1,  sometimes  called  the  coefficient  of  friction  of 
the  bearings.  The  sum  of  the  frictions  relative  to  the  2  supports  will 
be  the  product  of  fi  by  the  sum  of  the  pressures  which  the  shaft  exer- 
cises respectively  upon  them  —  a  sum  which  is  equal  to  the  resultant 
F  of  all  the  exterior  forces  applied  to  the  shaft  perpendicularly  to 
its  direction,  and  regarded  as  carried  parallel  to  themselves  to  a 
single  point  of  application. 

The  expression  of  the  friction  concerning  a  shaft  will  be,  then,  fiF, 
and  the  momentum  of  this  friction,  with  reference  to  the  axle  of  the 
shaft,  will  be  /ipF,  by  calling  p  the  diameter  of  the  shaft  (or  of  its 
journal,  if  there  be  one). 

The  second  resistance  is  called  the  roughness  of  the  cord,  and  con- 
sists in  this :  that,  for  want  of  sufficient  flexibility  of  the  cable,  the 
strip  through  which  the  resistance  acts,  and  which  enrolls  itself  upon 
the  pulley,  deviates  a  little  from  the  direction  of  the  latter,  in  such  a 
manner  as  to  increase  its  lever-arm,  and  consequently  its  movement. 


264  ROPE    TRANSMISSION. 

The  same  thing  does  not  take  place  in  the  other  strip,  whose  unroll- 
ing is,  on  the  contrary,  favored  by  the  elasticity  of  the  cord. 

Among  the  empiric  formulae  proposed  to  express  the  roughness,  we 
will  choose  that  which  represents  the  addition  of  the  lever-arm,  which 
it  creates  by  sA2,  A  being  the  diameter  of  the  cord  (or  thickness  of  the 
belt),  and  s  a  coefficient  depending  upon  the  material  of  which  it  is 
made. 

By  introducing  these,  the  equations  of  uniform  movement  become : 

For  the  conducting  or  motor  pulley, 

Pr  +  tR—T  (R  +  *A<)  —fif>F=  o ;  (4.) 

For  the  pulley  moved, 

Tr'—  t  (R+  6-A*)  —  Qr'-fo'F'  =  o.  (5.) 

r  r' 

As  here  we  have  no  longer  a  priori  P—  =Q  — ,,  there  are,  in  real- 

II         R 

ity,  3  unknown  quantities,  T,  t,  and  P,  or  rather  T,  t,  and  Q,  following 
which  we  get  either  Q  or  P.  3  distinct  equations  then  are  necessary. 
We  shall  find  them  by  uniting  the  equation  (3  a),  which  expresses 
the  condition  relative  to  the  tensions,  to  the  2  equations  (4)  and  (5), 
in  which  F  is  a  function  of  P  of  T  of  t,  and  of  the  weights  of  the 
pulley  A  and  of  its  shaft,  and  F'  a  function  of  Q,  of  T,  of  t,  and  of 
the  weights  of  the  pulley  B  and  of  its  shaft.  The  solution  of  the 
problem  is  then  possible,  theoretically  speaking.  It  is  for  belts  only 
that  one  can  consider  the  2  strips  as  each  one  being  rectilinear  and 
the  tension  uniform.  We  shall  see  that  for  cables  it  is  different. 
With  the  tensions  T  and  t  of  the  2  strips  [of  the  belt]  in  motion, 
there  corresponds  a  tension  0,  common  to  the  2  strips  at  rest.  This 
tension  at  rest  0  once  realized,  the  putting  in  motion  —  in  other  words, 
the  putting  in  play  of  the  power  and  of  the  resistance  —  creates  of 
itself  the  inequality  of  tension  required,  and  consequently  realizes  the 
values  T  and  t. 

Such  is,  briefly,  a  general  resume  of  the  theory  of  funicular  trans- 
mission. The  following  reason  will  show  how  we  were  led  to  obtain 
this  kind  of  transmission  by  metallic  cables. 

The  size  to  be  given  to  the  cable  is  equal  to  the  quotient  obtained 
by  dividing  T,  the  maximum  of  tension  which  it  has  to  undergo,  by 
the  number  which  represents  the  tension  compared  to  unity  of  a  sec- 
tion which  the  material  permits.  But  the  constructor  makes  the  size 
of  T  only  to  a  certain  limit.  In  effect,  omitting  the  passive  resistances 


ROPE    TRANSMISSION.  265 

which  would  uselessly  complicate  the  question,  we  find,  by  combining 
the  equations  (1)  and  (3  a), 


Let  v  be  the  speed  of  the  cord,  and  v'  that  of  the  point  of  applica- 

r       v' 
tion  of  P,  we  have  —  =  -  .    In  addition,  let  P  represent  the  direct 

action  of  the  first  motor  (as,  for  example,  if  the  latter  were  a  hy- 
draulic wheel,  mounted  upon  its  shaft  A),  let  it  represent  an  action 
transmitted  by  the  latter  by  means  of  gearing,  or  otherwise,  we  have, 

75  N 
by  calling  N  the  force  in  horse-power  of  the  first  motor,  P  =  —  —  . 

v 
Then  by  substituting 


Thus  the  power  to  be  transmitted  being  given,  the  tension  of  the 
cable  will  be  in  inverse  ratio  to  its  speed.  By  increasing  the  speed, 
the  constructor  may  make  the  section  smaller.  By  referring  to  equation 
(6)  it  will  be  easy  to  take  account  of  the  limit  of  mechanical  powers 
which  can  be  transmitted  by  a  given  cable.  For  this  we  must,  to 

begin  with,  take       _      as  the  value  of  those  cases  which  require 

the  least  tension.  Now  we  know  that  k  =  eSa,  a  being  the  smaller  of 
the  two  arcs  of  enrolment.  These  are  the  greatest  values  of  /  and 
of  a  which  are  to  be  regarded  here.  The  smaller  of  the  two  arcs 
of  enrolment  cannot  exceed  a  semi-circumference,  and  by  taking 
account  of  the  deviation  caused  by  the  roughness,  we  can  value  it  at 
0,95o.  The  maximum  of  /for  belts  is  about  0,30.  Then  the  value 
of  k  will  be  2,448.  For  that  of  /i,  we  will  admit  its  maximum  to  be 

unity.     We  will  have  then       **_      =  1,69. 

Of  the  other  part,  we  can  scarcely  think  of  increasing  the  speed  of 
the  belt  to  more  than  25  metres,  nor  to  run  it  permanently  at  a  rate 
of  more  than  Ok,25  per  square  millimetre  of  a  section.  If  we  wish 
to  find  what  power  we  can  transmit  on  these  conditions  with  a  belt 
having  a  breadth  of  250  millimetres,  and  a  thickness  of  8  millimetres,* 

*  It  is  certain  that  belts  of  more  than  8  millimetres  in  thickness  are  often 
employed.  But  then  the  force  resulting  from  the  flexion  of  enrolment  acquires 
a  notable  value,  which  diminishes  the  margin  allowed  for  the  effort  resulting 
from  the  general  tension.  It  would  be  necessary  to  admit  for  this  latter  a  num- 
ber inferior  to  Ok,2o  in  such  a  way  that,  in  the  point  of  view  of  power  trans- 
mitted, little  would  be  gained. 


266  ROPE    TRANSMISSION. 

which  is  already  a  strong  belt,  we  would  have  to  solve  the  equation : 
£50.8. 0,25=  1,69. 7-^-^, 

which  gives  N  =  9&|  horse-power  nearly.  (=40.97  n' of  surface 
velocity.) 

If  we  had  taken  account  of  passive  resistances,  and  had  allowed 
for  ft  a  number  <  1,  and  for  the  adhesion  of  the  belt  to  the  pulley, 
less  favorable  conditions,  which  use  brings  sooner  or  later,  we  would 
have  obtained  a  figure  sensibly  less. 

What  precedes  suffices  to  show  that  transmission  by  belts  is  only 
applicable  to  limited  mechanical  powers.  But  even  within  these 
limits,  the  greatness  of  the  distance  becomes  an  obstacle  to  its  em- 
ployment. Experience  has  shown  that  the  elasticity  of  the  belt 
causes  oscillations  and  variations  of  speed,  which  increases  with  the 
distance,  and  which,  beyond  a  certain  limit,  would  render  the  trans- 
mission very  irregular.  Besides,  where  it  would  be  necessary  to 
make  the  agent  of  transmission  pass  over  a  great  distance  in  the 
open  air,  a  belt  would  be  in  a  bad  state  of  preservation.  The  search 
for  an  agent  of  transmission,  at  the  same  time  supple  and  not  too 
elastic,  having  sufficient  resistance,  and  not  very  liable  to  alter,*  was 
then  indicated  with  a  view  of  transmitting  great  mechanical  powers 
to  a  distance. 

This  desideratum  has  been  realized  by  the  invention  of  metallic 
cables,  due,  as  we  know,  to  Mr.  Ch.  F.  Hirn,  of  Col  mar. 

The  Telo-Dynamic  System.     By  C.  F.  Him. 

182»  "  For  the  transmission  of  power  or  '  work '  to  moderate 
distances,  we  have  had  for  ages  two  main  methods  employed  —  the 
horizontal  revolving  shaft  and  the  strap  pulley  —  supposing,  as  is 
almost  always  the  case,  that  what  we  need  in  the  form  of  the  trans- 

*  As  to  the  question  of  cost,  we  can  say  that,  according  to  average  statements, 
a  section  of  a  funicular  organ,  capable  of  supporting  a  continual  strain  of  100 
kilogrammes,  arising  from  the  general  tension,  costs,  per  running  metre,  for 

Leather francs  3.50. 

Caoutchouc "     4.25. 

Wire  (rope) "     0.40. 

To  compare  these  prices,  in  a  practical  point  of  view,  it  would  be  necessary  to 
introduce  a  coefficient  of  duration  for  each  substance.  But  this  comparison 
would  be  of  no  account,  except  between  the  leather  and  the  caoutchouc ;  for 
there  would  be  no  competition  between  the  employment  of  the  latter  and  me- 
tallic cables. 


ROPE    TRANSMISSION.  267 

mitted  work  is  rotatory  motion  ;  but  these  are  only  capable  of  trans- 
mitting work  to  extremely  short  distances,  unless  with  the  most  seri- 
ous losses  or  waste  of  power  by  the  absorption  of  work  of  the  motor 
in  torsion  and  friction  of  the  shaft,  and  in  friction,  rigidity,  and  slip, 
etc.,  of  the  strap." 

"  For  a  mere  dead  pull,  such  as  the  alternate  strokes  needed  to 
work  a  pump,  work  is,  and  has  long  been,  transmitted  to  very  great 
distances ;  as  by  the  long  lines  of '  draw  rods '  used  in  mining  regions 
for  transmitting  the  power  of  a  water-wheel  by  means  of  a  crank  on 
its  main  axis,  pulling  during  half  its  revolution  to  raise  a  heavy 
weight  or  '  balance  bob '  at  the  remote  end  of  the  line  of  bars ;  but  a 
system  of  draw  rods  cannot  economically  be  employed  in  producing 
rotatory  motion  at  great  distances. 

"In  recent  days,  the  idea  so  clearly  seen  by  Bramah  has  been 
realized  upon  a  large  scale  by  Armstrong  and  others,  in  the  trans- 
mission of  power  by  water  pressure,  or,  as  it  has  been  called,  by 
*  hydraulic  connection ; '  and  Armstrong  has  even  perfected  appa- 
ratus by  which  water  pressure  thus  transmitted,  through,  it  might  be, 
miles  of  pipe,  may  be  converted  into  rotatory  motion." 

"  Papin  saw  the  possibility  of  transmitting  power  through  pneu- 
matic connectors,  though,  if  the  accounts  handed  down  be  reliable, 
he  did  not  succeed  in  realizing  his  notions.  There  can  be  no  ques- 
tion, however,  that  power  may  be  transmitted,  either  by  exhaustion 
or  by  the  condensation  of  air,  for  very  great  distances  through  tubes, 
and  may  be  converted  into  rotatory  motion  at  the  remote  extremity, 
or  anywhere  by  the  way.  .  .  . 

"  In  both  these  cases,  like  that  of  the  hydraulic  connector,  how- 
ever, unless  the  tubes  bear  a  very  large  proportion  in  area  to  the 
demand  for  the  current,  whether  of  entering  or  of  issuing  air  that 
transmits  the  power,  the  loss  by  tube  friction  becomes  very  serious. 
The  capital  to  be  sunk  in  pipes,  therefore,  is  large  in  relation  to  the 
power  got,  and  both  this  expenditure  and  the  waste  of  power  increase 
directly  with  the  distance  of  transmission." 

"  Meanwhile,  however,  there  exists  in  actual  use,  and  upon  a  large 
scale,  another  and  a  simpler  apparatus  for  the  transmission  of  power, 
in  large  amount  and  to  very  great  distances,  which  has  attracted,  we 
may  say,  no  attention  as  yet  in  this  country.  We  refer  to  the  system 
originated  by  Mr.  C.  F.  Hirn,  which  has  been  called  that  of  '  telo- 
dynamic  transmission,'  and  some  drawings  indicative  of  which  were 
shown  as  long  ago  as  the  Exhibition  of  1862." 

"  Crudely  stated,  this  method  appears  to  the  superficial  observer  to 


268  ROPE    TRANSMISSION. 

consist  in  nothing  more  than  in  transmitting  the  rotatory  motion  of 
one  large  grooved  pulley,  kept  revolving  by  the  motor,  to  another 
such  pulley,  at  a  greater  or  less  distance,  by  the  intervention  of  an 
endless  wire  or  steel  band,  or  wire  rope,  passing  over  both  pulleys ; 
and  to  the  uninstructed  observer  the  whole  affair  seems  nothing  more 
than  the  old  '  belt  and  pulley,'  a  mere  elongation  of  that  common- 
place '  wrapping  connector.'  The  hidden  principle  involved,  how- 
ever, is  something  entirely  different. 

"  If  we  suppose  a  band  of  round  iron  of  one  inch  in  diameter  to  be 
capable  of  sustaining  a  steady  pull,  without  sensible  alteration,  of  10 
tons,  and  that  the  bar  be  pulled  with  this  force  endways,  so  that  a 
point  between  the  motor  and  the  resistance  moves  at  the  rate  of  one 
foot  per  second,  then  it  is  obvious  that  the  bar  itself  will  be  trans- 
mitting '  work '  at  the  rate  of  10  foot-tons  per  second.  A  bar  of  half 
its  diameter,  or  \  its  section,  can  only  be  strained  to  2.5  tons,  and  at 
the  same  rate  of  *  end-on '  motion,  can  only  transmit  2.5  foot-tons  of 
work  per  second ;  and  so  also  of  a  bar  \  of  an  inch  diameter,  or  3\- 
of  the  area  of  the  one-inch  bar,  it  can  only  transmit  .04  ton ;  and,  at 
the  rate  of  one  foot  per  second,  .04  foot-tons  of  work.  But  suppose 
that  the  half-inch  bar  moves  end-on  at  the  rate  of  4  feet  per  second, 
and  that  the  i-inch  diameter  wire  moves  at  the  rate  of  25  feet  per 
second,  then,  as  work  is  made  up  of  pressure,  times  velocity,  all  3 
bars,  much  as  they  differ  in  section  and  in  absolute  strain  upon  each, 
will  transmit  the  same  number  of  foot-tons  per  second  :  i.  e.,  shall  all 
be  capable  at  the  resisting  end  of  delivering  forth  equal  quantities  of 
motive  power  in  equal  times.  If,  therefore,  we  increase  the  velocity 
of  motion  of  the  wrapping  connector,  which  is  intended  to  transmit 
a  given  amount  of  motive  work  in  a  given  time,  we  may  reduce  its 
section,  because  we  have  reduced  the  strain  upon  it,  and  hence  its 
total  weight  in  the  inverse  ratio  of  the  increased  velocity.  We  may, 
in  fact,  to  put  an  extreme  illustration,  reduce  the  one-inch  round  bar 
to  an  iron  wire,  as  fine  as  a  human  hair,  and  yet  (theoretically)  get 
out  of  it  at  the  resisting  end  our  10  foot-tons  per  second." 

"Now,  this  is  just  the  principle  which  distinguishes  Mr.  Hirii's 
method  from  any  common  belt  and  pair  of  pulleys,  and  which  he  has 
shown  can  be  carried  into  practical  use  with  great  advantage. 

"  At  the  motor,  be  it  steam-engine  or  water-wheel,  he  places  a  tol- 
erably large  cylindrical-grooved  rimmed  iron  pulley,  revolving  in  a 
vertical  or  horizontal  plane,  to  which  he  communicates  rotation  at  a 
determinate  and  considerable  speed.  Round  this  he  passes  a  thin 
wire,  or  a  thin  wire  rope  (which  latter  in  practice  he  prefers),  and 


ROPE    TRANSMISSION.  269 

this  is  led  away  to  almost  any  reasonable  distance  (the  limit  is  meas- 
urable by  miles),  where  it  is  passed  over  another  similar  pulley,  and 
returns  back  as  an  endless  cord  to  the  pulley  whence  it  started.  If 
the  distance  be  more  than  a  few  hundred  feet,  or  the  intervening  sur- 
face differ  in  level,  etc.,  both  limbs  of  the  cord  are  supported  and 
guided  at  intervals  by  guide  pulleys,  as  few  as  possible,  leaving  the 
cords  in  the  intervals  between  these  to  sag  down  into  such  catenary 
as  the  strains  upon  it  and  its  own  surplus  strength  may  determine 
and  admit.  The  periphery  of  the  driving  pulley  may  have  an  angu- 
lar velocity  as  great  as  possible ;  the  only  limit,  in  fact,  is  that  the 
speed  shall  not  be  likely  to  destroy  the  pulley  by  centrifugal  force. 
The  speeds  that  have  been  actually  employed  in  the  examples  to 
which  we  are  about  to  refer  vary  from  10  to  30  yards  per  second,  at 
the  circumference  of  the  pulley.  The  pulleys  themselves  have  been 
made  of  cast-iron  and  of  steel,  and  they  have  but  one  peculiarity  of 
construction,  and  that  is  a  highly  important  one.  At  the  bottom  of 
the  acute  V-shaped  groove,  going  round  the  circumference,  a  little 
trough  is  formed,  dove-tailed,  in  section,  which  is  filled  with  a  ring 
of  softened  gutta-percha  let  into  it,  and  united  at  the  returned  ends. 
Against  this,  as  the  bottom  of  the  V  groove,  the  wire  rope  of  trans- 
mission alone  bears.  It  forms  a  seat  for  itself,  and  does  not  touch 
the  sides  of  the  V  groove  or  other  metallic  parts  of  the  pulley.  The 
same  arrangement  is  adopted  for  the  receiving  pulley  for  the  power 
at  the  remote  end,  and  for  all  guide  or  supporting  pulleys  that  may 
be  necessary. 

"  The  wire  ropes  are  thus  found  to  hold  perfectly,  and  not  to  wear 
sensibly,  for  long  periods. 

"  Previously  to  devising  this  form  of  pulley,  Mr.  Him  had  had 
much  difficulty  from  the  wear  of  the  wire  ropes,  and  in  other  ways, 
and  had  tried,  in  vain,  wood,  copper,  and  other  linings  for  the  pulley 
grooves. 

"  Now,  assigning  a  peripheral  velocity  to  the  motor  pulley  of  30 
yards  per  second,  it  is  obvious,  upon  the  principles  we  have  already 
stated,  that  for  each  horse-power  that  we  require  to  transmit,  we 
must  visit  a  strain  upon  the  material  of  the  cord,  moving  at  that  rate, 
of  £3^°£=  say  366  Ibs. ;  and  taking  the  breaking  strain  for  average 
iron  wire  at  67,000  Ibs.  per  circular  inch,  and  the  safe  strain  at  about 
J  that,  or  say  33,000  Ibs.  per  circular  inch,  then  ^f  £ g£  =  90  nearly, 
or  a  wire  of  ^0  of  a  circular  inch  in  area  will  transmit  a  horse-power 
per  second. 

"  The  wire  must  have  surplus  strength,  however,  also,  for  the  loss 


270  ROPE    TRANSMISSION. 

of  power  absorbed  by  the  sources  of  loss  in  this  method  of  trans- 
mission. These  are :  1,  the  resistance  of  the  air  to  the  rotation  of 
all  the  pulleys ;  2,  the  rigidity  of  the  wire  rope  in  circumflexure  of 
the  2  main  pulleys,  and  through  the  change  of  angular  direction  at 
either  side  of  supporting  or  guide  pulleys ;  3,  the  resistance  of  the 
air,  by  friction,  to  the  passage  of  the  wire  cord  itself  through  it;  4, 
the  friction  of  the  axles  of  all  the  pulleys. 

"  Where  the  distances  of  transmission  are  moderate,  i.  e.,  within 
a  few  hundred  yards,  the  actual  result  of  experiments  upon  the  large 
scale,  as  stated  by  Mr.  Him,  show  that  all  these  together  amount  to 
about  2^  per  cent,  of  the  power  transmitted.  Where  supporting  and 
guide  pulleys  are  required,  there  is  to  be  added  to  this  2±  per  cent., 
which  represents  a  constant  resistance  due  to  the  motor  and  trans- 
mitting pulleys  and  rope  merely,  an  additional  resistance  which  varies 
with  the  distance,  and  has  been  found,  with  the  usual  amount  of 
supporting  or  guiding  pulleys  needed  for  long  distances,  to  amount 
to  about  504  foot-pounds  for  each  1100  yards  in  length  of  the  double 
cord.  Thus  we  see  that  for  short  distances  the  transmitting  wire 
need  not  be  larger  than  g^  of  a  circular  inch  in  area  per  horse- 
power; and  for  even  such  an  extreme  distance  as  upwards  of  12 
miles,  we  need  only  add  ^  to  its  total  area,  on  account  of  all  resist- 
ances due  to  uselessly  consumed  power. 

"  Enough  has  been  said  to  show  how  attenuated  may  be  the  trans- 
mitting cord,  and  how  light  it  may  be. 

"With  2  pulleys,  each  of  12  feet  diameter,  making  100  Rpm,  and 
with  a  wire  cord  of  -f-  of  an  inch  in  diameter,  Mr.  Hirn  has  found 
that  120  horse-power  can  be  transmitted  to  a  distance  of  150  yards, 
with  only  a  waste  of  power  or  useless  effect  of  2|  horse-power. 

"The  first  attempt  at  practical  application  of  this  method  was 
made  as  long  ago  as  1850,  at  Logelbach,  near  Colmar,  at  the  ancient 
Calico  print-works  of  MM.  Haussmann,  established  in  1772,  but 
shut  up  from  1841.  It  was  proposed  to  make  the  great  concern  into 
a  weaving  factory  for  cotton,  but  the  immense  scattered  mass  of 
buildings  seemed  to  forbid  the  possibility  of  utilizing  them,  and  yet 
placing  the  motive  power  at  any  one  point.  Shafting,  as  a  matter 
of  cost  and  of  waste  by  distance,  was  out  of  the  question. 

"  In  this  emergency  Mr.  Hirn  first  tried  this  method  of  force  trans- 
mission, with  a  riveted  steel  ribbon  or  band  to  each  building  from 
the  engine-house.  The  band  first  tried  was  about  2  inches  wide  by 
^'-5-  of  an  inch  thick,  and  on  wood-faced  drums.  The  success  of  the 
principle  was  complete,  but  much  remained  to  be  discovered  before 


ROPE    TRANSMISSION.  271 

the  round  wire  cord  and  gutta-percha  pulley  solved  all  difficulty,  and 
brought  the  principle  to  be  a  practical  reality. 

"  Since  the  establishment  of  MM.  Haussmann's  weaving- mills  on 
this  plan,  in  1854,  M.  Schlumberger  has  transmitted  the  power  of  a 
turbine  at  Staffelfelden  about  90  yards ;  in  1857,  at  Copenhagen,  45 
horse-power  was  transmitted  to  saw-mills  at  more  than  1000  yards 
distance  from  the  motor ;  in  1858,  at  Coruimont,  Vosges,  50  horse- 
power was  transmitted  to  a  distance  of  1258  yards;  in  1859,  at 
Oberursel,  near  Frankfort-ou-the-Main,  100  horse-power  was  thus 
carried  1076  yards ;  and  at  Emmendingen,  Brisgau,  60  horse-power 
works  a  spinning-mill  at  1312  yards  from  the  motor;  while  in  1861, 
Count  d'Espremesnil,  at  Fontaine  le  Sonet,  Department  de  1'Eure, 
transmitted  a  very  large  power  to  saw-mills  through  1100  yards,  and 
thence  a  part  to  a  farther  distance  of  546,  or  to  a  total  of  1646  yards, 
to  drive  other  machinery. 

"  400  and  upwards  of  practical  applications  have  been  made  of  the 
method  already ;  which  has  become  one  of  the  established  and  recog- 
nized mechanical  appliances  all  through  the  south-east  of  France  and 
adjacent  Germany,  and  more  particularly  in  Alsace,  the  great  seat 
of  the  French  cotton  manufacture,  and  of  innumerable  connected 
industries. 

"  Most  of  the  machinery  has  been  constructed  by  Messrs.  Stein  & 
Co.,  of  Mulhausen,  who  have  acquired  great  experience  in  its  con- 
structive details  and  management.  And,  carrying  the  principle  out 
to  its  legitimate  end  and  development,  a  company  has  been  formed 
since  1862,  at  Bale,  in  Switzerland,  under  the  title  of  '  Compaguie 
d'Utilization  des  forces  du  Rhin  Superieur,'  whose  object  it  is  to 
establish  water-power  to  an  almost  limitless  extent  at  the  great  fall 
of  the  Rhine  at  Schaffhausen,  and  thence  to  transmit  it  off  to  great 
distances  and  in  various  directions,  and  let  it  off  for  manufacturing 
uses.  Mr.  Hirn  has  shown  that  power  may  be  practically  and  profit- 
ably transmitted  thus  for  distances  of  several  miles.  To  take  an 
extreme  example,  he  proves  that  120  horse-power  may  be  transmitted 
22,000  yards,  or  about  12^  miles,  and  that  the  loss  by  uselessly 
expended  power  in  the  transmission  even  to  that  extreme  distance, 
shall  leave,  at  the  very  least,  90  horse-power  available  at  the  remote 
end.  On  the  other  hand,  he  shows  that  if  200  horse-power  be  trans- 
mitted by  ordinary  horizontal  shafting,  50  per  cent,  of  the  motor  will 
become  uselessly  absorbed  within  a  distance  of  1650  yards,  and  that 
to  obtain  100  horse-power  at  the  remote  end  of  a  horizontal  shaft  12^ 
miles  long,  we  must  apply  at  the  motor  end  a  power  of  788,400  horse- 


272  ROPE    TRANSMISSION. 

power  :*  in  other  words,  that  while  the  limit  of  shaft  transmission 
practically  does  not  exceed  200  or  300  yards,  that  of  telo-dynamic 
transmission  need  not,  in  practice,  stop  at  5  miles,  or  even  more. 
Power  may  thus  be  transmitted  economically  and  surely,  in  any 
direction,  over  hills  and  valleys,  across  rivers,  into  the  depths  of  coal 
pits  or  mines." —  Practical  Mech.  Jour.,  March,  1867,  p.  358. 

Telo-Dynamic  Transmission. 

1S3»  We  give  only  those  parts  which  add  new  facts  to  the  state- 
ments already  made  in  an  article  on  this  subject. 

"The  wheels  are  made  as  light  as  is  consistent  with  strength,  not 
only  for  the  sake  of  reducing  the  inertia  of  the  moving  mass,  and 
the  friction  on  the  axes  to  a  minimum,  but  for  the  more  important 
object  of  diminishing  the  resistance  of  the  air.  It  can  hardly  be 
doubted  that  an  abandonment  of  spokes  entirely,  and  making  the 
pulley  a  plain  disc,  would  improve  essentially  the  performance,  could 
discs  be  made  at  once  strong  enough  to  fulfil  the  required  function 
and  light  enough  not  materially  to  increase  the  friction.  It  will  be 
seen  further  on  that  the  resistance  of  the  air,  which  Mr.  Him  admits 
to  be  equal  to  the  sum  of  the  other  resistances,  is,  in  fact,  more  than 
double  all  the  rest  put  together. 

"  This  figure,  which  is  a  half  size  cross  section  of  the  rim,  C,  of  the 
wheel,  represents  the  form  of  the  groove  into  which  the 
armature,  B,  of  gutta-percha  is  compacted,  and  upon 
which  the  wire  rope,  A,  rests.    The  dove-tail  enlargement 
of  this  groove  at  the  base  is  necessary,  not  merely  to 
secure  the  gutta-percha  against  displacement  by  ordi- 
~.      17       nary  causes,  but  to  prevent  its  being  detached  by  cen- 
trifugal force.     Mr.  Hirn  assumes  30  metres  per  second 
to  be  the  velocity  which  it  is  expedient  ordinarily  to  give  to  the  cir- 
cumference of  the  wheel ;  but  he  has  carried  this  occasionally  as  high 
as  40  metres. 

"  At  30  metres,  the  centrifugal  force  generated  at  the  circumference 
of  the  smaller  pulleys  of  2  metres  in  diameter,  will  be  between  90 
and  100  times  the  force  of  gravity ;  and  at  40  it  will  be  nearly  170 
times  gravity.  That  is  to  say,  as  the  circumference  of  such  a  wheel 
measures  a  little  over  20  feet  around,  if  each  foot  of  this  circum- 
ference weighs  one  pound,  the  whole  will  be  dragged  in  all  directions 
with  this  last  velocity  by  forces  which  unitedly  will  amount  to  nearly 

*  Compare  with  Webber's  tests  of  shafting,  on  page  20. 


HOPE    TRANSMISSION.  273 

1|  tons.  It  is  on  this  account  that  Mr.  Him  suggests  that  the  limit 
of  30  metres  had  better  not  be  overpassed,  higher  velocities  endan- 
gering the  destruction  of  the  wheel. 

"  The  invention  of  Mr.  Him  was  first  applied  in  the  transmission 
of  moderate  powers  to  moderate  distances. 

"  Instead  of  a  cable  there  was  used  in  the  beginning  a  band  of 
steel,  having  a  breadth  of  about  2J  inches,  and  a  thickness  of  ^ 
of  an  inch.  This  presented  two  inconveniences.  In  the  first  place, 
on  account  of  its  considerable  surface  it  was  liable  to  be  agitated  by 
the  winds ;  and,  secondly,  it  soon  became  worn  and  injured  at  the 
points  where  it  was  riveted. 

"  It  served,  however,  very  well,  for  18  months,  to  transmit  12  horse- 
power to  a  distance  of  80  metres. 

"  A  cable  was  then  substituted,  and  this,  first  introduced  in  1852, 
is  still  in  good  condition. 

"  These  applications  have  been  made  for  the  most  part  in  France, 
and  in  the  department  in  which  the  invention  originated,  but  there 
are  some  notable  exceptions." 

"In  the  great  government  manufactory  of  gunpowder  at  Okhta,  in 
Russia,  which  was  destroyed  in  1864  by  explosion,  it  was  determined 
in  the  reconstruction  of  the  works  to  erect  the  buildings  at  such  a 
distance  from  each  other  that  the  explosion  of  one  of  them  should 
not  involve,  as  happens  usually  in  such  cases,  the  ruin  of  all  the 
rest. 

"  This  new  manufactory,  which  went  into  operation  in  1867,  is  corn- 
posed  of  34  different  workshops  or  laboratories,  to  which  motive 
power  is  transmitted  from  3  turbines,  having  a  total  force  of  274 
horse-power  along  a  line  nearly  a  mile  in  length. 

"  Several  establishments  in  Germany  employ  it  for  distances  vary- 
ing from  350  to  1200  metres.  An  officer  of  the  Danish  navy  has 
made  one  application  of  it  on  a  line  of  1000  metres,  and  at  the 
mines  of  Falun,  in  Sweden,  more  than  100  horse-power  is  transmitted 
by  it  to  a  distance  of  5000  metres. 

"  The  cost  of  the  machinery  and  its  erection  is  estimated  at  5000 
francs  per  kilometre,  exclusive  of  the  necessary  constructions  at  the 
termini,  which  will  require  an  additional  expenditure  of  25  francs 
per  horse-power.  In  the  case  of  100  horse-power  carried  10  kilo- 
metres, the  total  expense  will  therefore  amount  to  52,500  francs. 

"  For  its  practical  value,  this  invention,  simple  as  it  appears,  is  one 
of  the  most  important  that  has  presented  itself  in  the  Exposition, 
and  the  jury  have  shown  that  they  so  regard  it,  by  awarding  to  the 
18 


274  HOPE    TRANSMISSION. 

inventor  the  distinction  of  a  grand  prize." — F.  A.  P.  Barnard,  LL.D., 
U.  S.  Commissioner  to  Paris  Exposition,  1867. 

Wire-Rope  Driving. 

184.  "  Among  the  more  recent  improvements  in  the  way  of  trans- 
mitting power  for  long  distances,  is  the  substitution  of  belts  by  endless 
wire  ropes,  running  at  a  high  speed.  Their  use  bids  fair  to  add  im- 
mensely to  our  manufacturing  facilities.  The  distance  to  which  you 
can  thus  transfer  power  ranges  from  75  feet  to  4  miles.  Just  where 
the  belt  becomes  too  long  for  economy,  there  the  rope  steps  in.  In 
place  of  a  flat-faced  pulley,  a  narrow  sheave,  with  a  deep,  flaring 
groove  is  used,  the  groove  being  filled  out,  or  lined,  rather,  with 
leather,  oakum,  India-rubber,  or  some  other  soft  substance,  to  save 
the  rope.  The  essential  points  are  a  large  sheave,  running  at  a  con- 
siderable velocity,  and  a  light  rope. 

"  When  the  distance  exceeds  400  feet,  a  double-grooved  wheel  is 
used,  and  a  second  endless  rope  transmits  the  power  400  feet  farther, 
and  so  on  indefinitely.  The  loss  by  friction  is  about  8  per  cent,  per 
mile.  A  few  examples  may  prove  of  interest,  and  give  information. 

"  It  is  required  to  transmit  300  horse-power  by  means  of  a  wire 
rope.  A  wheel  14^  feet  diameter,  making  108  Rpm,  is  sufficient  — 
the  rope  running  at  a  rate  of  4920  Fpm.  Size  of  rope  required,  one 
inch  diameter.  The  distance  has  nothing  to  do  with  it.  Again :  '  It 
is  desired  to  transmit,  for  any  distance,  as  much  power  as  a  12-inch 
belt  will  give.'  Assuming  that  the  belt  travels  in  the  neighborhood 
of  1300  Fpm,  it  is  about  equivalent  to  20  horse-power;  and  a  grooved 
sheave  of  7  feet  diameter,  running  100  Rpm,  with  a  f-inch  rope,  will 
be  the  proportions  required.  Again :  a  4-feet  wheel,  running  100 
Rpm,  with  a  |-inch  rope,  will  convey  from  4  to  5  horse-power.  The 
cost  of  the  rope  is  always  the  smallest  item,  amounting  to  a  few  cents 
per  foot,  and  not  one-tenth  the  cost  of  an  equivalent  amount  of  belt- 
ing. 

"  One  is  thus  enabled,  at  a  small  expense,  to  transmit  power  in  any 
direction ;  for  instance,  to  a  building  lying  remote  from  the  main 
factory  buildings,  where  it  is  not  worth  while  to  put  up  a  separate 
engine ;  across  rivers,  creeks,  canals,  streets ;  over  the  tops  of  houses ; 
under  water ;  from  cellar  to  roof,  etc. 

"  Frequently  an  excellent  site  for  water-power  remains  unimproved 
for  want  of  suitable  building  sites  in  the  neighborhood.  The  water 
may  be  conveyed  down  stream  by  means  of  expensive  canals  and 
flumes ;  but  by  a  wire  rope  transmission  we  can  transfer  it  in  any 


ROPE    TRANSMISSION. 


275 


direction,  either  up  stream,  across  it,  or  sidewise,  up  and  down  grades 
of  one  in  8  —  in  fact,  anywhere. 

"  In  many  sections  of  our  country,  coal  is  dear  and  water-power 
plenty,  but  not  improved,  for  reasons  which  may  be  set  aside  by  the 
above  method.  In  Europe,  over  1000  factories  are  driven  in  that 
way." — The  Manufacturer  and  Builder,  February,  1869,  p.  38. 

Note  on  the  Sheaves  Used  in  the  Transmission  of  Power 
by  Wire  Ropes. 

185.  The  writer  found  in  his  practice  that  it  was  not  only  neces- 
sary to  have  the  rims  and  grooves  of  the 
wheels  truly  turned,  the  wheels  balanced 
for  running  without  vibration  in  their 
bearings,  but  that,  also,  some  certain  pro- 
tection must  be  furnished  to  prevent  the 
rope  striking  against  the  flanges  of  the 
wheels,  to  which  it  is  constantly  liable 
by  the  cross  action  of  air  currents,  by 
the  irregular  wearing  of  the  gum  filling, 
and  by  the  vibration  of  the  wheels. 

In  Fig.  77,  an  efficient  and  inexpen- 
sive method  of  preserving  the  rope  is 
shown,  by  lining  the  sides  of  the  wheel- 
groove  flanges,  A,  with  leather,  B,  se- 
cured by  copper  rivets  above  the  gum 
filling,  and  held  firmly  by  the  filling  in 
the  groove. 

Rope  Gearing. 

1SO»  In  a  paper  by  Mr.  John  Ramsbottom,  in  Newton's  Journal, 
Vol.  XXI.,  p.  46,  on  traversing  cranes  at  Ore  we  Locomotive  Works, 
dated  January  28,  1864,  mention  is  made  of  the  means  by  which 
power  is  communicated  from  the  shop  lines  of  shafting  to  the  gear 
of  the  cranes. 

"  It  consists  of  a  |-iuch  diameter,  soft,  white-cotton  cord,  weighing 
about  1^  ounces  to  the  foot,  running  at  the  rate  of  5000  Fpm,  in  a 
line  with  the  longitudinal  motion  of  the  crane,  above  the  same,  and 
over  a  4-feet  diameter  tightener  sheave.  This  sheave  is  weighed  so 
as  to  put  a  tension  on  each  strand  of  the  cord  of  108  Ibs.,  which  is 
found  to  be  the  best  working  strain  for  keeping  the  rope  steady,  and 
giving  the  required  'hold'  on  the  main  driving  pulley. 

"  The  cranes  have  a  span  of  40  feet  7  inches,  a  longitudinal  trav- 
erse of  270  feet,  and  the  rails  are  16  feet  above  the  floor. 


Fig.  77. 


276  ROPE    TRANSMISSION. 

"  The  cord  is  supported  every  12  or  14  feet  by  cast-iron  fixed  slip- 
pers of  plain  trough  section,  l|-inch  wide,  with  side  flanges.  These 
slippers  are  placed  1£  inches  below  the  working  line  of  the  driving 
side  of  the  cord,  so  as  to  allow  the  driving  wheels  on  the  traverser  to 
pass  them.  They  are  not  oiled,  and  the  friction  of  the  cord  in 
them  amounts  to  f  of  the  working  load. 

"  Motion  is  communicated  to  the  gear  of  the  crane  by  pressing  the 
cord  into  grooved  cast-iron  pulleys.  The  grooves  in  the.  driving  pul- 
leys are  V-shaped,  at  an  angle  of  30°,  and  the  cord  does  not  touch 
bottom.  The  guide  pulleys  have  circular  grooves,  same  diameter  as 
the  cord,  and  the  pressure  pulleys  have  a  circular  groove  of  larger 
diameter  than  the  cord.  The  driving  pulleys  have  a  diameter  equal 
to  30  times  the  diameter  of  the  rope.  Guards  are  put  on  the  pulleys 
to  keep  the  ropes  in. 

"  The  driving  power  of  the  cord  to  lift  25  tons  is  only  18  Ibs.,  irre- 
spective of  friction,  which  is  a  ratio  of  3111  :  1.  Light  loads  are 
about  800  :  1.  In  the  gib  cranes,  driven  by  similar  means,  the  ratio 
is  1000  :  1,  when  lifting  4  tons  at  the  rate  of  5  feet  1^  inches  per 
minute. 

"  The  actual  power  required  to  lift  9  tons,  besides  the  snatch-block 
and  chain,  has  been  found  to  be  17  Ibs.  at  the  circumference  of  the 
driving  pulley.  The  crab,  when  unloaded,  requires  1J  Ibs.  to  over- 
come its  friction. 

"  The  cords  are  soon  reduced  to  ^-inch  diameter,  and  last  about  8 
months  at  constant  work. 

"  In  an  overhead  traverser,  used  in  the  boiler-shop,  lifting  6  tons, 
3  years  in  use,  a  f-inch  cord  was  employed,  but  was  afterwards 
changed  for  a  cord  ^-inch  in  diameter. 

"  The  light  driving  cord  is  the  only  plan  compatible  with  high 
speeds  —  a  heavy  chain,  belt,  or  cord  would  soon  wear  out  and 
break  by  its  own  weight." 

Iron  and  Steel  Ropes  Compared. 

187.  The  superintendent  of  Cedar  Point  Iron  Company,  Port 
Henry,  N.  Y.,  says,  in  reference  to  the  comparative  merits  of  steel 
and  iron  wire  ropes  for  hoisting  purposes : 

"  We  have  used  iron  and  steel  wire  ropes  extensively  at  our  iron 
ore  mines,  and  our  experience  in  hoisting  from  1000  to  1500  tons 
gross  per  day  awards  the  superiority  by  all  odds  to  steel.  One 
steel  rope  lasts  us,  on  an  average,  as  long  as  6  iron  ones. 

"  We  attempted  to  run  them  on  same  sheaves  as  we  had  used  for 


ROPE    TRANSMISSION.  .  277 

iron  ropes,  and  found,  in  some  cases,  that  the  steel  rope  would  cut  one 
inch  into  the  cast-iron  sheaves  in  one  or  two  mouths  of  use. 

"  Our  sheaves  now  are  lined  with  wood,  which  entirely  obviates 
every  difficulty  in  the  use  of  steel,  and  of  course  is  equally  to  be  com- 
mended for  iron." —  January,  1873. 

On  Rope  Gearing  for  the  Transmission  of  Large  Power  in  Mills 
and  Factories.     By  Mr.  James  Durie.* 

188.  The  best  means  of  transmitting  power  from  the  prime 
mover  to  the  various  machines  in  a  factory  has  long  been  a  matter 
of  importance  to  the  engineer  and  to  the  manufacturer.  Until  lately, 
toothed  gearing  —  either  as  spur  or  bevel  wheels,  or  a  combination 
of  both  —  has  been  almost  universally  employed  for  first  motions, 
the  smaller  powers  being  taken  off  pulleys  by  leather  belts.  The 
facility  of  taking  small  powers  off  drums  to  machines  by  means  of 
belts,  and  the  absence  of  noise  and  vibration,  led  to  the  adoption,  in 
the  United  States  of  America,  of  broad  leather  belts  for  the  transmis- 
sion of  large  powers  from  the  prime  mover  to  the  shafting  in  facto- 
ries ;  and  the  success  which  has  followed  the  adoption  of  these*  large 
belts  there,  has  led  to  their  being  adopted  by  many  users  of  power  in 
this  country. 

The  object  of  the  present  paper  is  to  bring  before  the  institution 
the  plan  of  transmitting  large  powers  by  means  of  round  ropes  work- 
ing on  grooved  wheels,  which,  in  some  parts  of  this  country,  has  been 
largely  adopted  as  a  substitute  for  toothed  gearing.  The  experience 
gained  by  the  firm  with  which  the  writer  is  connected,  in  this  mode 
of  transmitting  power,  has  extended  over  a  period  of  thirteen  years ; 
and  wherever  it  has  been  employed,  either  to  replace  toothed  gearing 
in  old  or  for  new  works,  it  has  always  given  complete  satisfaction. 

In  this  mode  of  driving,  the  fly-wheel  of  the  engine  is  made  con- 
siderably broader  than  the  fly-wheel  of  an  engine  having  cogs  on  its 
circumference;  and,  instead  of  cogs,  a  number  of  parallel  grooves  for 
the  ropes  are  turned  out,  the  number  and  size  of  which  are  regulated 
by  the  power  to  be  taken  off  the  fly-wheel.  The  power  which  each 
of  the  ropes  will  transmit  depends  upon  their  size,  and  the  velocity 
of  the  periphery  of  the  fly-wheel.  The  ropes  employed  are  of  two 
sizes  for  large  powers,  namely,  5^  inches  and  6J  inches  circumference; 
another  size  of  rope,  4|  inches  circumference,  is  employed  for  small 


*  A  paper  read  at  the  meeting  of  the  Institution  of  Mechanical  Engineers,  at 
Manchester,  England,  October  25,  1876.     From  Iron,  London,  Oct.  28,  1876. 


278  ROPE    TRANSMISSION. 

powers,  but  there  is  no  definitely  ascertained  limit  to  the  size  of  ropes 
that  may  be  employed.  Where  large  powers  are  required,  and  where 
large  pulleys  can  be  used,  it  is  best  to  use  heavy  ropes,  and  the  con- 
trary when  the  opposite  is  the  case. 

The  velocity  of  the  periphery  of  the  grooved  fly-wheel  and  pulleys 
is  generally  arranged  to  be  between  3000  and  6000  Fpm ;  and  the 
velocity  being  settled,  and  the  power  of  the  steam-engine  known,  the 
number  of  the  ropes  required  to  transmit  the  power  is  then  deter- 
mined, from  the  experience  that  has  been  gained  of  the  amount  of 
power  transmitted  by  ropes  in  previous  cases.  It  is  very  essential 
that  the  right  proportion  between  the  diameter  of  the  ropes  and  the 
pulleys  is  obtained ;  if  the  diameter  of  the  pulley  is  too  small,  the 
rope,  in  continually  bending  over  them,  is  apt  to  strain  the  strands 
and  grind  the  core  into  dust,  and  on  the  size  of  the  pulley  in  a  great 
measure  depends  the  life  of  the  rope.  As  a  general  rule,  the  cir- 
cumference of  a  pulley  should  not  be  less  than  30  times  that  of  the 
rope  which  works  on  it.  In  apportioning  the  distance  between  the 
driver  and  the  driven  shafts,  great  latitude  may  be  taken  —  a  dis- 
tance of  from  20  to  60  feet  may  be  taken  as  a  fair  space. 

The  mode  of  applying  a  complete  system  of  rope  gearing  may  be 
seen  at  a  factory  for  spinning  and  weaving  jute  belonging  to  Messrs. 
A.  &  J.  Nicoll,  at  Dundee,  and  fitted  up  by  Messrs.  Pearce  Bros., 
Lily  bank  Foundry,  of  that  town ;  this  gearing  has  been  working 
from  June,  1870.  The  engine  fly-wheel  is  22  feet  diameter,  and  has 
18  grooves  cut  in  its  circumference;  its  width  is  4  feet  10  inches 
over  all.  The  engine  makes  43  Rpm,  and  the  velocity  of  the  periph- 
ery of  the  fly-wheel  is  2967  Fpm.  The  power  of  the  engine  varies 
from  400  to  425  indicated  horse-power;  the  power  transmitted  by 
each  of  the  ropes,  which  are  6^  inches  circumference,  is,  therefore, 
about  23  horse-power.  The  power  is  transmitted  to  the  ground 
floor  by  5  ropes  on  to  a  pulley  7  feet  6  inches  diameter,  the  power 
required  being  115  indicated  horse-power;  that  to  the  first  floor  by 
4  ropes  to  a  pulley  5  feet  6  inches  diameter,  the  power  required 
being  92  indicated  horse-power;  and  that  to  the  attic  by  6  ropes  on 
to  a  pulley  5  feet  6  inches  diameter,  the  power  required  being  138 
indicated  horse-power;  2  shafts  being  required  in  this  room,  the 
power  to  the  second  shaft  is  transmitted  by  horizontal  ropes,  whilst 
on  the  other  side  of  the  engine  shaft  3  ropes  transmit  69  indicated 
horse-power  to  a  weaving  shed,  the  pulley  being  7  feet  6  inches 
diameter.  The  ropes  should  never  be  so  heavily  loaded  as  to  draw 
them,  even  on  short  spans,  to  a  near  approach  to  a  straight  line;  in 


HOPE    TRANSMISSION.  279 

this  factory  each  rope,  travelling  at  a  velocity  of  2967  Fpm,  trans- 
mits, as  above,  23  indicated  horse-power,  the  tension  on  the  rope  is, 

„       33,000x23        0_  .       . 

therefore, =  zoo  IDS.,  which  is  a  very  long  way  under 

2967 

the  breaking  strength  of  the  ropes. 

The  ropes  do  not  rest  on  the  bottom  of  the  groove,  but  on  its  V-- 
shaped sides ;  these  sides  are  generally  made  at  an  angle  of  about 
43°  to  each  other.  If  the  angle  at  which  the  grooves  are  formed  is 
very  obtuse,  the  ropes  will  slip ;  if  too  acute,  much  friction  may  be 
caused  by  the  rope  becoming  wedged  into  the  groove.  As  the  sum 
of  the  tensions  upon  the  two  parts  of  a  band  is  the  same,  whatever 
be  the  pressure  under  which  the  band  is  drawn  or  the  resistance 
overcome,  the  returning  side  of  the  rope  is  as  much  slackened  as  the 
working  side  is  tightened.  It  is,  therefore,  generally  advisable,  when 
it  can  be  so  arranged,  to  have  the  tight  or  driving  side  of  the  ropes 
at  the  bottom,  so  that  the  returning  side  may  lap  round  the  top  of 
the  pulleys,  and  consequently  obtain  extra  bearing  surface ;  when 
the  opposite  is  the  case,  the  ropes  fall  sooner  out  of  the  grooves,  and 
so  lessen  the  bearing  surface.  It  is  not  always  practicable  to  arrange 
this;  and  in  the  case  of  taking  the  power  off  both  sides  of  the  driving 
pulley,  it  is  obviously  impossible. 

None  of  the  shafts  of  this  factory  are  driven  from  the  fly-wheel 
by  less  than  3  ropes,  the  strain  on  each  rope  being  only,  as  shown 
above,  256  Ibs. ;  it  may  therefore  be  supposed  that  a  greater  weight 
may  temporarily  be  put  upon  a  rope,  in  case  any  of  the  ropes  should 
require  to  be  tightened  up,  and  this  is  often  done.  A  rope  is  taken 
off  at  a  meal  hour,  respliced,  and  put  on  again  at  the  next  stoppage 
of  the  engine,  thus  avoiding  any  necessity  for  night  work  or  over- 
time. Night  work  should  always  be  avoided,  for  besides  the  extra 
expense  incurred,  the  work  is  never  so  well  done  by  artificial  light 
as  by  daylight. 

In  the  Samnuggur  Jute  Factory,  Calcutta,  which  is  a  one-story 
building,  all  the  machinery,  both  spinning  and  weaving,  is  on  the 
ground  floor.  The  engines  are  placed  near  the  middle  of  the 
building;  they  are  about  1000  indicated  horse-power,  and  make 
43  Rpm ;  the  fly-wheel  is  28  feet  diameter,  and  its  width  6  feet  7 
inches ;  the  velocity  of  the  periphery  being  3784  Fpm.  The  ropes 
are  6J  inches  circumference,  18  ropes  transmit  the  power  to  the 
right  hand  or  spinning  side,  and  7  ropes  to  the  left  hand  or  weaving 
side,  making  a  total  of  25  ropes ;  each  rope  therefore  transmits  40 


280  ROPE    TRANSMISSION. 

indicated  horse-power.     The  tension  on  each  rope  due  to  this  load  at 

the  above  velocity  is  —  —  =  349  Ibs.,  which  is  rather  a  heav- 

3784 

ier  load  than  in  the  previously  described  factory ;  all  the  shafts  are 
also  driven  by  more  than  one  rope,  with  the  exception  of  some  of  the 
line  shafts  in  the  weaving  shed.  Rope  gearing  was  only  adopted  in 
this  case  after  the  most  searching  inquiry  as  to  its  suitability  for 
working  in  the  warm  and  humid  climate  of  Calcutta,  and  its  adop- 
tion has  been  attended  with  very  satisfactory  results,  both  in  this 
case  and  also  at  the  Sealdah  Mills  in  Calcutta. 

The  drawings  show  the  arrangements  adopted  when  the  factories 
have  been  specially  designed  for  rope  gearing ;  but  this  gearing  has 
often  been  applied  to  replace  toothed  gearing  in  mills  already  built. 
The  plan  then  adopted  is  to  put  in  a  new  grooved  fly-wheel,  or  to 
place  grooved  segments  upon  the  existing  fly-wheel,  when  the  speed 
is  sufficiently  great  to  allow  of  a  limited  number  of  ropes  being 
employed,  and  the  width  of  the  wheel-pit  is  also  sufficient  for  the 
purpose;  but  if  this  plan  cannot  be  adopted,  grooved  pulleys  are  put 
on  the  second-motion  shaft,  and  the  ropes  carried  to  the  different 
stories  of  the  mill.  It  has  even  sometimes  been  necessary  to  put  in 
a  counter  shaft,  so  as  to  gain  speed  and  get  sufficient  length  between 
the  centres  of  the  shafts  on  which  the  pulleys  are  placed. 

A  comparison  has  now  to  be  made  between  the  system  of  rope 
gearing  and  the  other  2  systems  in  use  at  the  present  time.  The 
system  in  most  general  use  is  toothed  gearing ;  in  this  the  first  driver 
is  the  spur  wheel  fitted  on  to  the  crank  shaft  of  the  engine,  into 
which  is  geared  the  driven  pinion  of  smaller  size.  In  order  to  insure 
these  2  wheels  working  well,  it  is  absolutely  essential  that  the  cen- 
tres of  the  engine  shaft  and  the  shaft  of  the  pinion  are  rigidly  fixed 
at  the  correct  distance  from  each  other,  and  that  the  teeth  of  the  2 
wheels  are  accurately  of  the  same  pitch  and  size.  The  first  of  these 
objects  is  obtained  by  making  the  engine  bed,  in  a  horizontal  engine, 
a  strong  rigid  casting  resting  on  an  expensive  ashlar  foundation,  or 
in  a  beam  engine  the  foundations  are  alone  depended  upon.  If  these 
objects  are  obtained,  the  wheels  ought  to  work  smoothly  and  without 
much  noise ;  but  how  often  this  desirable  object  is  obtained,  it  only 
requires  a  walk  to  be  taken  through  the  streets  of  a  manufacturing 
town,  to  ascertain  by  the  rumbling  noise,  sometimes  heard  at  a  dis- 
tance of  several  hundred  yards,  that  all  is  not  as  it  should  be  for  the 
safe  and  economical  transmission  of  the  power  of  the  steam-engine. 
If  the  factory  consists  of  more  than  one  story,  the  power  has  to  be 


ROPE    TRANSMISSION.  281 

taken  from  the  second-motion  shaft,  by  means  of  an  upright  shaft 
and  bevel  wheels,  requiring  heavy  wall  boxes,  and  strong  walls  to 
keep  the  wall  boxes  in  their  places;  the  whole  object  in  the  construc- 
tion of  the  factory  being  to  secure  a  rigid  and  immovable  structure, 
a  matter  which  is  very  difficult  to  attain. 

In  the  case  of  rope-gearing,  the  ropes  by  which  the  power  is  trans- 
mitted consist  of  an  elastic  substance,  and  their  lightness,  elasticity, 
and  comparative  slackness  between  the  pulleys,  are  highly  conducive 
to  their  taking  up  any  irregularity  that  may  occur  in  the  motive 
power.  This  accounts  for  the  slight  attachments  that  are  required  for 
shafting  driven  by  ropes  from  a  grooved  fly-wheel ;  and  it  is  the  same 
with  all  the  bearings  throughout  the  mill,  the  shafts  in  the  various 
flats  only  requiring  a  light  wall-box,  bracket,  or  the  bearing  may  be 
carried  on  a  column  of  the  mill.  The  cost  of  fitting  up  a  mill  with 
rope  gearing  is  considerably  less  than  with  tooth  gearing,  when  the 
shafts  to  be  driven  revolve  at  a  high  speed,  but  the  cost  is  about  the 
same  in  other  cases.  It  is,  however,  rather  difficult  to  give  exact 
figures  for  this  comparison,  one  great  saving  being  in  the  foundations 
of  the  engine,  the  wall-boxes,  and  the  extra  strength  of  the  walls 
required  for  upright  shafts. 

The  great  advantage  of  rope  gearing,  however,  is  the  entire  free- 
dom from  any  risk  of  a  breakdown ;  when  a  rope  shows  symptoms 
of  giving  way  —  and  ropes  always  give  symptoms  of  weakness  long 
before  they  break  —  the  weak  rope  can  be  removed,  and  another  put 
in  its  place  at  any  meal  hour  or  evening.  The  cost  of  the  mainte- 
nance of  ropes  for  transmitting  400  indicated  horse-power  has  been 
found  to  be  £20  per  annum,  or  about  £5  per  100  indicated  horse- 
power per  annum.  This  is  made  up  of  the  cost  of  renewal  of  the 
ropes,  and  occasional  wages  for  tightening  them.  Some  ropes  have 
been  found  to  run  10^  years ;  but,  as  the  general  rule,  the  life  of  a 
rope  may  be  said  to  be  from  3  to  5  years,  though  even  5  years  have 
been  often  much  exceeded. 

The  friction  of  rope  gearing  has  often  been  found  to  be,  for  high 
speeds,  considerably  less  than  that  of  toothed  gearing ;  but  the 
writer  regrets  not  being  able  to  give  definite  information  on  this 
point,  which  is  a  very  important  one  to  those  contemplating  altering 
their  gearing  or  building  new  works.  The  reason  why  no  definite 
reason  can  be  given  - —  beyond  the  universal  impression  of  those  who 
have  adopted  them,  that  ropes  require  less  power  to  drive  than 
toothed  gearing  —  is,  that  in  all  cases  where  rope  gearing  has  been 
substituted,  other  alterations  have  been  made  at  the  same  time,  or 


282  ROPE    TRANSMISSION. 

the  engines  were,  after  the  alteration,  driven  at  an  extra  speed  of  10 
or  15  Rpm.  However,  every  one  who  has  substituted  rope  gearing 
for  toothed  gearing,  also  agrees  in  bearing  testimony  to  the  great 
improvement  and  steadiness  of  driving  obtained  after  the  alteration, 
and  that  they  are  enabled  to  turn  off  a  greater  amount  of  yarns  from 
the  machinery  in  the  same  time.  The  tendency  at  the  present  time, 
with  the  introduction  of  shorter  hours  of  labor  and  foreign  competi- 
tion, being  to  increase  the  speed  of  shafting  and  machinery,  to  be 
able  by  this  means  to  increase  the  speed  of  the  shafts  must  be  of  great 
advantage  to  those  who  own  old  mills,  the  toothed  gearing  of  which  is 
generally  driven  as  fast  as  it  is  safe  to  drive  it. 

The  ropes  used  for  rope  gearing  are  mostly  made  of  hemp,  carefully 
selected ;  the  qualification  of  a  good  rope  being  that  the  fibres  are  as 
long  as  possible,  and  that  the  rope  should  be  well  twisted  and  laid, 
and  yet  be  soft  and  elastic.  It  is  also  very  important  that  the  ends 
of  the  ropes  should  be  united  by  a  uniform  splice  —  the  splice  should 
not  be  of  a  greater  diameter  than  the  other  part  of  the  rope  ;  to  effect 
this  object  the  splice  is  made  about  9  or  10  feet  long. 

The  comparison  between  rope  gearing  and  toothed  gearing  having 
been  made,  it  remains  to  compare  ropes  and  leather  belts,  which 
Matter  have  been  largely  used  in  the  manufacturing  districts  of  Lan- 
cashire and  Yorkshire,  for  the  transmission  of  large  powers.  The 
writer  has  not  been  able  to  obtain  very  satisfactory  information  as  to 
the  amount  of  power  absorbed  in  friction  by  large  belts ;  in  some 
cases  it  has  been  said  to  be  more,  and  in  some  less,  than  with  toothed 
gearing.  The  most  trustworthy  information  he  has  obtained  is  in  the 
case  of  a  4-story  woollen  mill,  where  an  upright  shaft,  with  bevel 
gearing,  was  replaced  by  2  belts,  one  22  inches  wide,  and  the 
other  27  inches  wide,  the  power  transmitted  being  400  indicated 
horse-power,  and  the  speed  of  the  belts  3000  Fpm.  The  driving 
pulleys  are  on  the  second-motion  shaft.  In  this  case  the  power 
is  stated  to  be  the  same  with  the  belts  as  it  was  before  the  alteration ; 
but,  as  in  the  case  of  rope-driving,  the  "  turning "  is  found  to  be 
much  superior  to  what  it  was  before  the  alteration.  The  width  of  the 
pulleys  for  ropes  is  generally  rather  less  than  for  belts  transmitting 
the  same  power ;  but  there  is  some  difference  of  practice  as  to  the 
width  of  belt  used  for  transmitting  a  certain  power.  The  cost  of 
hemp  ropes  is  considerably  less  than  of  leather  belting,  the  cost 
of  hemp  ropes  being  about  Is.  per  Ib.  against  3s.  per  Ib.  for 
leather  belts.  The  grooved  pulleys  for  ropes  cost  more  than  plain 
pulleys;  but,  making  allowance  for  this,  the  total  cost  of  ropes 


HOPE    TRANSMISSION.  283 

and  grooved  pulleys  for  transmitting  a  given  power,  does  not  exceed 
one-half  or  two-thirds  the  cost  of  leather  belting  and  flat  pulleys. 
The  advantage  of  ropes  over  belting,  however,  lies  in  the  power 
being  divided  up  into  a  number  of  ropes,  so  that,  in  the  case  of  any 
one  of  the  ropes  showing  symptoms  of  weakness,  that  rope  may  be 
removed  by  stopping  the  engine  for  a  few  minutes,  the  remaining 
ropes  continuing  to  do  the  work  until  a  stoppage  of  the  engine  occurs. 
In  the  case  of  belting,  as  only  one  belt  is  employed  to  drive  one  flat 
of  a  mill,  if  anything  were  to  occur  to  the  belt  the  whole  of  that  flat 
would  be  stopped  until  the  belt  was  repaired. 

Judging  from  the  practice  adopted,  the  comparative  amount  of 
power  transmitted  by  certain  sizes  of  ropes  and  widths  of  double 
belts,  the  writer  finds  that  a  6J-inch  circumference  rope  does  about 
the  same  amount  of  work  at  a  given  speed  of  say  3000  Fpm  as 
a  belt  4  inches  broad.  This  width,  however,  represents  the  smallest 
width  adopted  as  a  rule,  5  inches  corresponding  to  the  American 
practice ;  but,  taking  a  4-inch  belt,  the  bearing  surface  of  a  6|-inch 
circumference  rope  on  the  sides  of  the  grooves  on  a  4-feet  6-inch 
pulley  will  be  half  the  circumference,  or  85  inches,  and,  allowing 
the  rope  half  an  inch  width  of  bearing  on  each  side,  or  1  inch 
for  both  sides,  the  total  bearing  surface  is  85  x  1  —  85  square 
inches,  whilst  the  belt  has  85  x  4  —  340  square  inches,  or  4 
times  the  amount.  Consequently,  in  order  that  a  6^-inch  circum- 
ference rope  may  transmit  as  much  power  at  the  same  tension  as  a 
4-inch  belt,  the  effective  pressure  per  square  inch  of  the  bearing 
surface  of  the  rope  on  the  pulley  must  be  at  least  4  times  as  great 
as  that  of  the  belt. 

In  order  to  obtain  some  information  bearing  on  this  point,  a  set  of 
experiments  have  been  made  by  Mr.  A.  W.  Pearce,  at  Lilybauk 
Foundry,  Dundee,  the  results  of  which  are  given  in  the  following 
table.  The  experiments  were  made  with  the  materials  at  hand ; 
both  the  pulleys  were  just  as  they  came  from  the  lathe,  and  equally 
smooth,  and  they  were  nearly  the  same  size  as  named  in  the  table. 
Comparing  together  Nos.  2  and  5  experiments,  it  is  seen  that  a 
6-inch  circumference  ungreased  rope,  with  336  Ibs.  suspended  at 
one  end,  and  passing  over  a  4-feet  9-iuch  grooved  pulley,  which  was 
at  rest,  required  only  28  Ibs.  at  the  other  end  to  prevent  slipping; 
whilst  a  half-worn  good  single  leather  belt,  4  inches  wide,  with  the 
same  weight  at  one  end,  and  passing  over  a  4-feet  6-inch  pulley, 
required  113  Ibs.  at  the  other  end  to  prevent  slipping,  or  about  4 
times  as  much  as  with  the  rope.  The  bearing  surface  of  the  rope 


284 


ROPE    TRANSMISSION. 


would  be  only  about  one-fourth  that  of  the  belt,  and  the  effective 
pressure  per  square  inch  of  the  bearing  surface  of  the  rope  was 
consequently  in  this  case  16  times  as  great  as  that  of  the  belt.  In 
the  experiment  No.  4  a  double  leather  belt,  6  inches  wide  and  |  inch 
thick,  with  the  same  weight  at  one  end,  and  passing  over  a  4-feet 
6-inch  pulley,  required  98  Ibs.  at  the  other  end  to  prevent  slipping, 
or  3^  times  as  much  as  with  the  6-inch  circumference  rope.  The 
experiments  show,  however,  such  a  great  difference  between  the 
results  with  different  sizes  of  ropes  as  to  make  it  impossible  to  come 
to  any  definite  proportion  between  the  friction  of  ropes  and  belts ;  but 
they  show,  as  was  to  have  been  expected,  that  ropes  have  a  consider- 
ably greater  hold  on  the  V-shaped  grooves  per  square  inch  of  bearing 
surface  than  flat  belts  have  on  pulleys. 

Experiments  on  the  Friction  of  Ropes  and  Leather  Belts  on  Cast-Iron 
Turned  Pulleys. 


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NOTE. —  The  rope  pulley  used  in  these  experiments  was  grooved  for  6£-inch 
circumference  of  rope. 

The  writer  has  been  informed  that  in  the  United  States  several 
rolling-mills  are  driven  by  means  of  flat  leather  belts,  and  that  very 
satisfactory  results  are  obtained  by  their  use,  and  he  wishes  to  draw 
the  attention  of  members  engaged  in  this  department  of  manufacture 
to  the  suitability  of  rope  gearing  for  this  purpose.  Although  he  is 
not  aware  of  any  practical  example  of  its  having  been  applied  to 
driving  rolling-mills,  he  is  confident  that  from  the  slackness  with 
which  the  ropes  can  work,  and  the  hold  they  have  on  the  grooves  of 
the  pulleys,  they  would  be  admirably  adapted  for  taking  up  the 
shock  which  is  thrown  upon  the  gearing  of  a  train  of  rolls  when  the 
iron  enters  the  rolls. 

'Mr.  Welsh  opened  the  discussion  by  a  mathematical  criticism  of 


ROPE    TRANSMISSION. 


285 


the  principles  involved  in  the  paper,  arriving  at  a  corroboration  of 
the  angle  of  40°,  approved  by  Mr.  Durie,  on  the  ground  that  the 
tangent  of  half  this  angle  (0.364)  ought  to  be  equal  to  the  coefficient 
of  friction,  which,  taking  the  mean  of  the  writer's  experiments,  was 
0.399.  He  enforced  his  remarks  by  symbols  and  formulae  of  fearful 
complexity,  inscribed  upon  the  blackboard. 

Mr.  Paget  said  that  he  had  been  working  in  the  same  direction, 
and  had  performed  over  900  experiments  with  a  view  of  getting  at 
some  general  principle.  The  results,  however,  were  so  absurdly  dis- 
cordant that  he  had  abandoned  the  task.  His  best  results  corrobo- 
rated Mr.  Durie's  angle  of  40°. 

Transmission  by  Wire  Ropes  Used  as  Connecting-Rods. 
189.     On  each  of  the  shafts,  A  A,  Fig.  78,  are  arranged  3  cranks, 
each  120°  apart.     These  cranks  are  connected  by  wire  ropes,  which 


Fig.  78. 


286 


ROPE    TRANSMISSION. 


may  be  of  considerable  length  and  may  also  be  horizontal,  vertical, 
or  inclined,  as  the  location  demands. 

The  pulley,  E,  may  receive  the  power  from  the  motor,  and  D  may 
transmit  the  same  to  the  machinery  where  it  is  required. 

It  is  evident  that  the  distance  of  transmission  by  this  contrivance 
will  be  subject  to  the  sag  of  the  ropes  ;  but  the  rope  connections  may 
be  multiplied  by  the  use  of  intermediate  shafts,  and  in  that  way 
uniform  rotary  motion  may  be  transmitted  to  a  considerable  distance. 
The  motion  must  be  comparatively  slow,  however,  owing  to  the  severe 
strain  which  would  be  thrown  upon  the  bearings  by  the  surging  and 
swaying  of  the  ropes  during  the  rapid  changes  of  motion  to  which 


Fig.  79, 

they  would  be  liable ;  but  what  is  lost  in  velocity  may  be  gained  in 
power  transmitted  —  as  that  is  measured  by  the  strength  of  the  ropes 
—  and  it  is  ail  easy  matter  to  make  them  carry  heavy  burdens  safely. 
The  writer  saw  this  in  use  at  the  Whirlpool  Rapids,  Niagara,  for 
driving  the  passenger-elevator  recently  erected  at  that  place. 

Transmission  of  Rotary  Motion  by  Rods. 

190*  Reciprocating  motion  by  a  line  of  connecting-rods  and 
swinging  arms  for  working  pumps  and  the  like  is  old  and  in  common 
use  at  mines  and  quarries.  (See  page  267.) 

But  in  order  to  transmit  uniform  rotatory  motion,  limited  in  distance 


EOPE    TRANSMISSION.  287 

only  by  the  practical  working  length  of  rods,  the  devices  shown  in 
Fig.  79  may  be  employed. 

Two  eccentrics,  A  A,  set  at  right  angles  on  the  shaft,  D,  are  con- 
nected by  rods,  E  E,  to  two  cranks,  B  B,  which  are  also  secured  at 
right  angles  on  the  shaft,  C.  The  motion  transmitted  is  steady  and 
noiseless,  is  performed  in  the  same  direction  and  in  equal  time,  and 
is  very  suitable  for  valve-gears  in  steam-engines  and  the  like.  The 
effect  would  be  the  same  if  two  cranks  were  used  in  place  of  the 
eccentrics. 

The  writer  devised  and  applied  this  combination  of  well-known 
parts  to  driving  the  valve  cam-shaft  and  governor  of  a  beam  steam- 
engine  built  at  People's  Works,  Philadelphia,  in  the  year  1867. 


CHAPTER    IX. 
FRICTIONAL  GEARING, 

BY    E.    S.    WICKLIN.* 

19 !•  Frictioiial  gearing  is  the  term  applied  by  Webster  to  wheels 
that  transmit  motion  by  surface  contact,  without  teeth.  Among  me- 
chanics and  practical  men  who  build  and  use  them,  such  wheels  are 
usually  called  "  friction  gear."  When  spoken  of  separately,  that  is, 
without  reference  to  their  combination,  they  are  called  friction  "  pul- 
leys," especially  those  with  faces  parallel  to  the  axes.  When  made 
conical,  they  are  termed  "bevel  friction,"  and  are  usually  spoken  of 
as  "  wheels." 

This  style  of  gearing  is  now  in  use  in  the  lumbering  region  of  the 
north-west,  and  is  fast  gaining  favor  wherever  used.  It  has  some 
advantages  not  possessed  by  other  modes  of  communicating  motion, 
which  do  not  appear  to  be  counteracted  by  any  peculiar  disadvan- 
tages. As  a  rule,  however,  it  does  not  strike  the  mind  of  the  me- 
chanic favorably  when  first  suggested,  but  must  be  seen  to  be  appre- 
ciated. The  first  impression  appears  to  be  that  the  point  of  contact 
is  too  small  to  possess  any  considerable  amount  of  adhesive  force. 

*JOHN  H.  COOPER,  ESQ.,  PHILADELPHIA: 

Dear  Sir :  —  As  you  propose  to  publish,  in  your  "  TREATISE  ON  BELTING," 
an  article  on  Frictional  Gearing  written  by  me,  which  you  are  at  liberty  to  use,  I 
beg  to  add  a  word  of  explanation. 

These  papers  were  prepared  some  5  years  ago.  An  extensive  experience, 
however,  since  that  time,  with  this  method  of  transmitting  power,  has  but  con- 
firmed the  confidence  I  then  expressed  in  its  efficiency.  Pulleys  of  soft  maple, 
that  have  been  running  for  8  years,  and  that  have  transmitted  30  horse-power 
by  a  single  contact,  are  to-day  perfect.  Some  of  these  have  not  perceptibly  worn 
their  journals. 

Another  point  it  is  but  just  to  mention :  —  A  more  extended  acquaintance 
with  the  mills  of  the  north-west  has  shown  me  that  I  had  somewhat  overesti- 
mated the  extent  to  which  this  frictional  transmission  is  used.  Its  use,  though 
quite  general,  is  by  no  means  universal. 

Truly  Yours, 

E.  S.  WICKLIN. 
BLACK  RIVER  FALLS,  Wis.,  March  19, 1877. 

288 


FRICTIONAL    GEARING.  289 

It  is  generally  received  as  a  law  that  friction,  or  adhesion  of  contact, 
is  not  in  proportion  to  the  extent  of  contact,  but  to  the  amount  of 
pressure  and  the  condition  of  the  surfaces.  But  to  many  minds,  this 
law  appears  more  as  a  learned  theory  than  as  a  practical  truth.  In 
fact,  there  are  few,  even  of  our  best  mechanical  thinkers,  who  do  not 
manifest  some  surprise  when,  for  the  first  time,  they  see  with  what 
apparent  ease  one  smooth  wheel  will  drive  another  equally  smooth, 
by  what  appears  to  be  a  very  slight  contact ;  and  that  the  second 
wheel  is  not  only  itself  driven,  but  carries  with  it  ponderous  ma- 
chinery, involving  the  expenditure  often  of  more  than  50  horse- 
power. Nor  is  it  strange  that  many  minds  are  unprepared  for  such 
results,  since  most  of  our  mechanics  rely,  to  some  extent  at  least, 
upon  books,  in  the  absence  of  personal  experience ;  and  here  books 
fail. 

There  are,  perhaps,  no  other  means  of  transmitting  motion,  about 
which  so  little  has  been  written,  in  proportion  to  its  importance,  as 
frictional  gearing.  And  most  that  has  been  written  is  upon  the 
grooved  wheels,  which  are  frictional  to  their  injury,  and  are,  by  the 
unequal  motion  of  the  parts  in  contact,  as  well  calculated  to  absorb 
the  motive  power  as  they  are  to  destroy  each  other. 

As  examples :  In  the  latest  edition  of  Webster's  "  Unabridged  "  we 
find  the  following  definition  :  "Frictional  gearing,  wheels  which  trans- 
mit motion  by  surface  friction  instead  of  teeth.  The  faces  are  some- 
times made  more  or  less  V-shaped,  to  increase  or  decrease  friction,  as 
required." 

In  a  recent  work  on  mill  building,  perhaps  the  latest  published  in 
this  country,  a  work  of  large  pretensions,  the  only  allusion  to  this 
class  of  machinery  is  a  single  sentence,  in  the  chapter  on  friction,  as 
follows :  "  Friction  also  furnishes  a  convenient  medium  of  communi- 
cating and  transmitting  motion  in  machinery,  as  in  gigging  back  the 
carriage  and  log  in  saw-mills ;  and  in  some  modern  mills  the  whole 
driving  power  for  both  saws  and  mill-stones  is  communicated  by  fric- 
tion of  iron  upon  iron." 

Another  late  mechanical  work  gives  us  the  following  information 
upon  friction  gearing :  "  The  surfaces  of  the  wheels  are  made  rough, 
so  as  to  bite  as  much  as  possible." 

The  above  quotations  furnish  a  sample  of  what  may  be  learned 
from  books  of  this  very  important  mode  of  transmitting  motion. 
And  yet,  in  all  the  vast  lumbering  region  of  the  north-west,  com- 
prising a  large  part  of  2  or  3  States,  and  furnishing  building  and 
fencing  material  for  several  millions  of  people,  there  are  few  mills 
19 


290  FRICTIONAL,    GEARING. 

in  which  some  part  of  the  work  is  not  done  by  friction  gear ;  and  in 
many  mills  the  whole  power,  amounting  to  from  100  to  300  horse- 
power, is  thus  transmitted. 

The  growing  popularity  and  importance  of  this  rather  new  style 
of  gearing  cannot  fail  to  make  it  a  subject  of  interest  to  mechanical 
engineers  and  manufacturers. 

With  this  view,  the  writer  now  proposes  to  give,  in  a  short  series 
of  articles,  some  observations  taken  from  a  practical  standpoint,  and 
also  the  results  of  a  few  experiments,  made  to  determine  the  percent- 
age of  adhesive  force  or  traction  of  these  wheels  as  compared  with 
belted  pulleys. 

Now  a  word  as  to  what  friction  gearing  is,  where  it  has  become  an 
undoubted  success.  In  large  mills,  where  this  gearing  is  used  to 
transmit  power  to  drive  5  or  6  gangs,  one  or  2  large  circular  saws, 
a  muley,  gang-edgers,  trimmers,  slashers,  lath-mills,  shingle-mills, 
and  more  besides ;  where  20,000  feet  of  boards  may  be  sawn  in  an 
hour.  The  faces  of  the  wheels  are  not  "  made  more  or  less  V-shaped, 
so  as  to  increase  or  decrease  friction  as  required."  Nor  is  the  power 
"  communicated  by  the  friction  of  iron  upon  iron."  Neither  are  the 
surfaces  of  the  wheels  "  made  rough,  so  as  to  bite  as  much  as  pos- 
sible." On  the  contrary,  the  surfaces  are  made  smooth  and  straight 
as  possible ;  one  wheel,  or  pulley,  is  made  of  iron,  and  the  other  of 
wood,  or  of  iron  covered  with  wood.  So  it  is  seen  that  the  books  are 
wrong,  at  least  so  far  as  applied  to  the  localities  where  this  gearing 
is  most  used. 

Where  it  is  practicable,  this  gearing  is  so  arranged  that  the  wood 
drives  the  iron.  This  is  done  so  that  the  "slip,"  in  starting  up  ma- 
chinery while  the  driving  wheels  are  in  full  motion,  will  tend  to 
wear  the  wooden  wheel  round  rather  than  to  cut  it  in  grooves,  which 
is  done  to  some  extent  when  the  wheels  are  reversed,  though  this  ten- 
dency is  much  less  than  might  be  supposed,  as  in  most  cases  the 
"  bull  wheel,"  used  for  drawing  logs  into  the  mill,  is  a  large  wooden 
wheel,  driven  by  a  small  one  of  iron.  And  these  wheels,  though 
started  and  stopped  with  the  driver  in  full  motion  a  hundred  times 
a  day,  work  well  and  last  for  several  years.  But  for  machinery  in 
constant  use,  the  wooden  wheel  should  always  drive  the  iron. 

For  driving  heavy  machinery,  the  wooden  drivers  are  put  upon  the 
engine-shaft,  and  each  machine  is  driven  by  a  separate  counter-shaft. 
2  or  more  of  these  counter-shafts  are  usually  driven  by  contact  with 
the  same  wheel,  and  each  is  arranged  so  as  to  be  thrown  out  from 
the  driver  and  stopped  whenever  required,  and  again  started  at  any 


FRICTIONAL    GEARING.  291 

moment,  without  interference  with  other  machinery.  This  is  easily 
accomplished,  as  a  very  slight  movement  is  sufficient  for  the  purpose. 

To  drive  small  machinery,  these  friction  drivers  are  put  upon  a 
line-shaft,  so  as  to  drive  a  small  counter-shaft,  from  which  the  ma- 
chine is  driven  by  a  belt,  and  stopped  and  started  by  throwing  out 
the  counter-shaft,  and  throwing  it  in  again. 

To  select  the  best  material  for  driving  pulleys  in  friction  gearing 
has  required  considerable  experience,  nor  is  it  certain  that  this  object 
has  yet  been  attained.  Few,  if  any,  well-arranged  and  careful  exper- 
iments have  been  made  with  a  view  of  determining  the  comparative 
value  of  different  materials  as  a  frictional  medium  for  driving  iron 
pulleys.  The  various  theories  and  notions  of  builders  have,  however, 
caused  the  application  to  this  use  of  several  varieties  of  wood,  and 
also  of  leather,  India-rubber,  and  paper;  and  thus  an  opportunity 
has  been  given  to  judge  of  their  different  degrees  of  efficiency.  The 
materials  most  easily  obtained,  and  most  used,  are  the  different  varie- 
ties of  wood,  and  of  these  several  have  given  good  results. 

For  driving  light  machinery  running  at  high  speed,  as  in  sash, 
door,  and  blind  factories,  basswood  —  the  linden  of  the  Southern  and 
Middle  States  —  ( Tilia  Americana}  has  been  found  to  possess  good 
qualities,  having  considerable  durability  and  being  unsurpassed  in 
the  smoothness  and  softness  of  its  movement.  Cotton  wood  (populus 
moniliferci)  has  been  tried  for  small  machinery  with  results  somewhat 
similar  to  those  of  basswood,  but  is  found  to  be  more  affected  by 
atmospheric  changes.  And  even  white  pine  makes  a  driving  surface 
which  is,  considering  the  softness  of  the  wood,  of  astonishing  effi- 
ciency and  durability.  But  for  all  heavy  work,  where  from  20  to  60 
horse-power  is  transmitted  by  a  single  contact,  soft  maple  (acer  rubrum) 
has,  at  present,  no  rival.  Driving  pulleys  of  this  wood,  if  correctly 
proportioned  and  well  built,  will  run  for  years  with  no  perceptible 
wear. 

For  very  small  pulleys  leather  is  an  excellent  driver  and  is  very 
durable,  and  rubber  also  possesses  great  adhesion  as  a  driver ;  but  a 
surface  of  soft  rubber  undoubtedly  requires  more  power  than  one  of 
a  less  elastic  substance. 

Becently  paper  has  been  introduced  as  a  driver  for  small  machinery, 
and  has  been  applied  in  some  situations  where  the  test  was  most 
severe ;  and  the  remarkable  manner  in  which  it  has  thus  far  with- 
stood the  severity  of  these  tests  appears  to  point  to  it  as  the  most 
efficient  material  yet  tried. 

The  proportioning  of  friction  pulleys  to  the  work  required,  and 


292  FKICTIONAL    GEARING. 

their  substantial  and  accurate  construction  are  matters  of  perhaps 
more  importance  than  the  selection  of  material.  The  mechanic  who 
thinks  he  can  put  up  frictional  gearing  temporarily  and  cheaply  will 
make  it  a  failure.  Leather  belts  may  be  made  to  submit  to  all  man- 
ner of  abuse,  but  it  is  not  so  with  friction  pulleys.  They  must  be  most 
accurately  and  substantially  made,  and  put  up  and  kept  in  perfect  line. 

All  large  drivers  —  say,  from  4  to  10  feet  diameter  and  from  12  to 
30-inch  face  —  should  have  rims  of  soft  maple  6  or  7  inches  deep. 
These  should  be  made  up  of  plank,  1^  or  2  inches  thick,  cut  into 
"cants,"  g,  |,  or  y1^  of  the  circle,  so  as  to  place  the  grain  of  the  wood 
as  nearly  as  practicable  in  the  direction  of  the  circumference.  The 
cants  should  be  closely  fitted,  and  put  together  with  white  lead  or 
glue,  strongly  nailed  and  bolted.  The  wooden  rim,  thus  made  up  to 
within  about  3  inches  of  the  width  required  for  the  finished  pulley, 
is  mounted  upon  1  or  2  heavy  iron  "  spiders,"  with  6  or  8  radial 
arms.  If  the  pulley  is  above  6  feet  in  diameter,  there  should  be  8 
arms,  and  2  spiders  when  the  width  of  face  is  more  than  18  inches. 

Upon  the  ends  of  the  arms  are  flat  "pads,"  which  should  be  of  just 
sufficient  width  to  extend  across  the  inner  face  of  the  wooden  rim, 
as  described ;  that  is,  3  inches  less  than  the  width  of  the  finished 
pulley.  These  pads  are  gained  into  the  inner  side  of  the  rim,  the 
gains  being  cut  large  enough  to  admit  keys  under  and  beside  the 
pads.  When  the  keys  are  well  driven,  strong  "  lag  "  screws  are  put 
through  the  ends  of  the  arm  into  the  rim.  This  done,  an  additional 
"  round  "  is  put  upon  each  side  of  the  rim  to  cover  bolt-heads  and 
secure  the  keys  from  ever  working  out.  The  pulley  is  now  put  to  its 
place  on  the  shaft  and  keyed,  the  edges  trued  up,  and  the  face  turned 
off  with  the  utmost  exactness. 

For  small  drivers,  the  best  construction  is  to  make  an  iron  pulley 
of  about  8  inches  less  diameter  and  3  inches  less  face  than  the  pulley 
required.  Have  four  lugs,  about  an  inch  square,  cast  across  the  face 
of  this  pulley.  Make  a  wooden  rim,  4  inches  deep,  with  face  equal 
to  that  of  the  iron  pulley,  and  the  inside  diameter  equal  to  the  outer 
diameter  of  the  iron.  Drive  this  rim  snugly  on  over  the  rim  of  the 
iron  pulley,  having  cut  gains  to  receive  the  lugs,  together  with  a  hard 
wood  key  beside  each.  Now  add  a  round  of  cants  upon  each  side, 
with  their  inner  diameters  less  than  the  first,  so  as  to  cover  the  iron  rim. 
If  the  pulley  is  designed  for  heavy  work,  the  wood  should  be  maple, 
and  should  be  well  fastened  by  lag-screws  put  through  the  iron  rim ; 
but  for  light  work  it  may  be  of  basswood  or  pine,  and  the  lag-screws 
omitted.  But  in  all  cases  the  wood  should  be  thoroughly  seasoned. 


FRICTIONAL    GEARING.  293 

In  the  early  use  of  friction  gearing,  when  it  was  used  only  as  back- 
ing gear  in  saw-mills  and  for  hoisting  in  grist-mills,  the  pulleys  were 
made  so  as  to  present  the  end  of  the  wood  to  the  surface ;  and  we 
occasionally  yet  meet  with  an  instance  where  they  are  so  made.  But 
such  pulleys  never  run  so  smoothly  nor  drive  so  well  as  those  made 
with  the  fibre  more  nearly  in  a  line  with  the  work.  Besides,  it  is 
much  more  difficult  to  make  up  a  pulley  with  the  grain  placed  radi- 
ally, and  to  secure  it  so  that  the  blocks  will  not  split  when  put  to 
heavy  work,  than  it  is  to  make  it  up  as  above  described. 

As  to  the  width  of  face  required  in  friction  gearing :  When  the 
drivers  are  of  maple,  a  width  of  face  equal  to  that  required  for  a 
good  leather  belt  (single)  to  do  the  same  work  is  sufficient.  Or,  to 
speak  more  definitely,  when  the  travel  of  the  surface  is  equal  to  1200 
Fpm,  the  width. of  face  should  be  at  least  one  inch  for  each  horse- 
power to  be  transmitted,  and  for  drivers  of  basswood  or  pine  1^  to  2 
inches. 

The  driven  pulleys,  as  before  stated,  are  wholly  of  iron.  They  are 
similar  to  belt  pulleys,  but  much  heavier,  having  more  arms  and 
stronger  rim. 

The  arm  should  be  straight  rather  than  curved,  and  there  should 
be  2  sets  of  arms  when  the  face  of  the  pulley  is  above  16  inches.  For 
the  proportion  of  these  pulleys,  a  very  good  rule  is  to  make  the  thick- 
ness of  rim  2^  per  cent,  of  the  diameter ;  that  is,  when  the  pulley  is 
40  inches  diameter,  the  rim  should  be  an  inch  thick. 

To  secure  perfect  accuracy  these  pulleys  must  be  fitted  and  turned 
upon  the  shaft ;  and  when  large,  should  rest  in  journal  boxes  in  the 
latter  while  being  turned.  If  simply  swung  upon  the  lathe  centres, 
they  are  liable  to  vary  while  the  work  is  being  done.  When  turned 
exactly  true,  round,  and  smooth,  these  pulleys  must  be  carefully  and 
accurately  balanced.  The  neglect  of  this  last  essential  point  has 
worked  the  destruction  of  otherwise  well-made  friction  pulleys. 

When  thus  constructed  there  is  a  beauty  about  the  movement  of 
this  gearing  which  at  once  enlists  the  favor  of  all  who  can  appreciate 
the  "  music  of  motion,"  and  gives  character  to  its  builder.  Its  efficiency 
and  peculiar  advantages  will  be  more  fully  shown  further  on.  • 

In  the  practice  of  mechanics,  we  are  generally  satisfied  with  an 
old  and  familiar  principle,  without  giving  ourselves  any  great  trouble 
to  inquire  into  the  comparative  degree  of  its  efficiency.  But  this 
does  not  satisfy  the  requirements  of  science ;  nor  is  it  sufficient  for 
the  practical  mechanic  when  applied  to  principles  less  familiar. 

When  new  modes  are  introduced  as  rivals  of  the  old,  the  question 


294  FRICTIONAL    GEARING. 

of  comparative  efficiency  is  at  once  raised,  and  should  be  met  by 
crucial  experiment.  But  unfortunately  for  both  science  and  practice, 
these  questions  are  not  generally  so  met.  Too  few  experiments  are 
made,  and  those  without  sufficient  care  and  accuracy  to  establish 
principles  or  remove  doubts.  No  experiment  is,  however,  without 
some  degree  of  interest,  and  when  all  the  conditions  of  a  test  are 
known  it  is  not  difficult  to  estimate  approximately  the  value  of 
results.  With  this  view,  the  conditions  and  results  of  a  few  experi- 
ments, made  to  test  the  tractive  power  of  smooth-faced  friction  pul- 
leys, are  here  given.  These  experiments,  when  made,  were  not  meant 
for  publication  or  for  the  benefit  of  science,  but  to  establish  rules  for 
private  practice.  They  should  be  repeated  by  others  before  being 
taken  as  conclusive. 

For  the  experiments,  two  pulleys  were  made  in  the  usual  way,  one 
being  of  wood  —  soft  maple  —  and  the  other  of  iron.  Both  were 
accurately  and  smoothly  finished.  These  pulleys  were  each  17  inches 
in  diameter,  and  of  6  inches  face,  and  were  put  up  as  shown  in  the 
annexed  diagram. 


80. 


A,  in  the  diagram,  is  a  double  bell-crank  frame,  with  arms  2  feet 
long.  The  ends  of  the  upright  arms  receive  the  bearings  for  the  iron 
pulley,  I.  The  journals  of  this  pulley  are  1^  inches  in  diameter,  and 
3  inches  long,  and  run  in  Babbitt  boxes.  The  frame  is  hung  upon 
journals  or  trunnions,  T,  and  balanced  by  the  weight,  B.  Wand  P  are 


FRICTIONAL    GEARING. 


295 


strong  packing-boxes,  which  are  filled  with  scrap-iron  to  the  extent 
required.  The  face  of  the  pulley,  I,  is  extended  beyond  the  6  inches 
to  receive  the  cord,  C,  for  which  purpose  a  shallow  groove  is  cut  in 
the  pulley  so  as  to  bring  the  centre  of  the  cord  just  to  the  periphery. 
The  driving  pulley,  V,  is  put  upon  a  shaft  where  it  may  be  made  to 
revolve  slowly  in  the  direction  of  the  arrow. 

It  will  be  seen  that  the  weight  in  the  box,  P,  upon  the  horizontal 
arm  will  bring  the  pulleys  together  with  a  pressure  just  equal  to  the 
weight.  The  wooden  pulley  being  in  motion,  the  pressure,  when 
sufficient,  will  roll  the  other  pulley  and  raise  the  weight,  W. 

The  manner  of  experimenting  was  to  put  a  given  weight  upon  the 
cord,  C,  and,  while  the  driving  pulley  was  moving,  to  load  the  box, 
P,  until  the  weight,  W,  was  carried  up.  The  machinery  was  then 
stopped,  when  the  weight  would  slowly  descend,  slipping  the  iron 
pulley  backwards  upon  the  wood.  The  weight  in  the  pressure  box 
was  now  noted ;  the  weight  was  again  raised,  and  the  pressure  in- 
creased sufficiently  to  hold  the  weight  from  slipping  down,  and  the 
pressure  again  noted. 

In  the  following  table,  the  figures  on  the  left  show  the  weights 
raised.  The  second  column  gives  the  pressure  just  sufficient  to  bring 
the  weight  up ;  and  the  third  column  shows  the  weight  necessary  to 
raise  and  hold  the  weight,  without  slip. 


FRICTION  PULLEYS. 

BELTED  PULLEYS. 

PRESSURE  RE- 

PRESSURE RE- 

PRESSURE RE- 

WEIGHT 
RAISED. 

QUIRED  TO  JUST 
RAISE  THE 
WEIGHT. 

QUIRED  TO  RAISE 
THE  WEIGHT 

WITHOUT  SLIP. 

PRESSURE  RE- 
QUIRED TO  RAISE 
THE  WEIGHT. 

QUIRED  TO  RAISE 
THE  WEIGHT 
WITHOUT  SLIP. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

10 

29 

33 

30 

34 

20 

58 

65 

60 

69 

30 

87 

96 

91 

120 

40 

115 

125 

121 

159 

50 

143 

154 

153 

199 

60 

171 

185 

183 

242 

70 

199 

214 

213 

247 

80 

225 

244 

239 

332 

90 

264 

289 

278 

375 

100 

295 

312 

310 

419 

120 

354 

387 

372 

487 

140 

416 

438 

442 

563 

160 

477 

499 

524 

652 

180 

538 

561 

592 

731 

After  these  experiments  were  made  and  twice  repeated  with  the 


296  FRICTIONAL    GEARING. 

pulleys,  the  frame,  A,  was  reversed,  so  that  the  weight  in  the  pressure 
box  would  tend  to  separate  the  pulleys.  They  were  then  connected 
by  a  6-inch  leather  belt,  and  the  experiments  repeated  with  the 
results  given  in  the  fourth  and  fifth  columns  of  figures. 

It  will  be  seen  that,  in  this  test,  the  traction  of  the  friction  wheels 
was  greater  than  that  of  the  belted  pulleys,  and  considerably  more 
than  is  usually  supposed  to  be  obtained  from  belts  upon  pulleys  of 
either  wood  or  iron ;  and  that,  while  there  is  a  marked  falling  off  in 
the  adhesion  of  the  belt  as  the  work  increases,  that  of  the  friction 
increases  as  the  labor  becomes  greater.  Also,  that  the  difference  in 
the  pressure  required  to  just  do  the  work,  and  that  necessary  to  do  it 
without  loss  or  slip,  advances  in  an  increasing  ratio  with  the  work 
of  the  belt ;  but  in  the  friction  it  is  almost  constant  throughout  the 
whole  range  of  experiments.  The  figures  applied  to  the  friction 
wheels  are  the  mean  results  of  repeated  experiments ;  those  applied 
to  the  belted  pulleys  are  each  of  a  single  test.  It  is  not  thought  that 
these  experiments  were  sufficient  to  fully  establish  all  that  the  figures 
show ;  but  they  were  enough  to  prove  that  smooth-faced  wheels  pos- 
sess a  much  higher  tractive  power  than  has  been  generally  supposed. 
They  are  given  without  further  deduction  or  comment. 

And  now  a  word  as  to  some  of  the  advantages  of  friction  gearing. 
Being  always  arranged  with  a  movable  shaft,  so  that  the  wheels  may 
be  thrown  together  or  apart  with  the  greatest  ease,  the  machine 
driven  by  it  is  started  and  stopped  at  any  moment  while  the  driving 
wheel  remains  in  motion.  And  when  stopped,  the  separation  is  com- 
plete, and  may  so  remain  for  any  number  of  minutes  or  months  with- 
out attention,  and  may  be  again  started  at  any  moment  without  the 
least  inconvenience  or  injury.  So  slight  is  the  separation  required, 
that  it  is  done  almost  without  an  effort.  And  by  it  we  entirely  dis- 
pense with  the  nuisance  of  loose  pulleys,  belt  shifters,  and  idle  run- 
ning belts ;  and  with  the  risk  of  throwing  off  and  putting  on  belts. 
It  obviates  the  delay  and  labor  of  shipping  and  unshipping  pinions, 
and  the  rattle  and  bang  and  frequent  breaking  of  clutches.  It  is 
durable,  and  requires  no  repairs;  it  is  compact,  and  economizes  room. 
It  does  not  increase  the  pressure  on  journals  when  the  speed  is  quick- 
ened, as  is  the  case  with  belts  running  with  great  velocity,  but  remains 
constant  at  all  speeds.  And  it  will  transmit  any  amount  of  power, 
from  a  hundredth  part  of  a  horse-power  to  100  horse-power,  with  no 
greater  percentage  of  loss,  and  with  less  pressure  on  journals  than 
can  be  done  by  belts. 

It  is  not  contended  that  this  style  of  gearing  should  supersede  the 
belt.  There  are  hundreds  of  situations  in  which  nothing  can  take 


FRICTIONAL    GEARING.  297 

the  place  of  belts.  The  ease  with  which  they  can  be  carried  in  almost 
any  direction,  and  to  any  reasonable  distance,  will  perhaps  always 
place  them  foremost  as  a  means  of  transmitting  power.  But  where 
several  machines,  that  must  be  run  independently  of  each  other  and 
be  stopped  and  started  without  interference,  are  driven  by  the  same 
motor,  one  connection,  at  least,  should  be  frictional ;  and  that,  if 
practicable,  should  be  the  connection  nearest  the  motor.  Where  the 
motions  are  slow  and  the  occasions  for  stopping  few,  this  is  of  less 
importance  ;  but  where  the  speed  is  considerable,  and  the  stoppages 
are  frequent,  it  will  be  found  a  very  great  convenience. 

Since  the  introduction  of  friction  as  a  means  of  transmitting  motion, 
it  has  often  been  desirable  to  apply  the  principle  to  bevel  gearing. 
Frequently,  however,  this  has  been  unsuccessful.  The  failures  have 
resulted  either  from  the  want  of  a  correct  knowledge  of  the  principles 
of  bevel  gearing,  or  from  imperfect  workmanship  in  the  application 
of  those  principles. 

When  correctly  and  substantially  built  and  accurately  put  up, 
bevel  and  mitre  friction  pulleys,  within  certain  limits,  operate  just  as 
well  as  in  the  other  form.  True,  we  cannot  in  these,  as  in  the  cylin- 
drical pulleys,  extend  the  face  ad  libitum  without  greatly  increasing 
the  diameter ;  and  for  this  reason,  when  great  power  is  to  be  trans- 
mitted, it  is  not  convenient  to  use  this  form  of  gearing.  But  in  all 
fast  motions,  where  not  more  than  10  horse-power  is  to  be  transmitted, 
the  bevel  friction  is  one  of  the  best  means  of  connecting  at  an  angle. 
It  may  be  adapted  to  almost  any  change  of  speed,  and  set  to  any 
angle,  either  right,  obtuse,  or  acute,  and  has  the  same  advantages  in 
operation  as  the  other  form  of  friction.  And  when  it  is  required  to 
reverse  the  motion  at  pleasure,  it  is  most  conveniently  done  by  set- 
ting two  bevel  pulleys  upon  one  shaft,  facing  toward  each  other,  and 
placing  one  upon  another  shaft  between  them,  so  that  it  may  be 
brought  into  contact  with  either. 

In  building  this  gearing,  the  iron  cone,  or  pulley,  is  made  similar 
to  a  bevel  pinion,  except  as  to  the  teeth,  instead  of  which  there  is  a 
smoothly  turned  face.  The  same  care  should  be  bestowed  upon  the 
accuracy  of  finish  and  balance  that  is  required  in  the  other  form  of 
friction  pulley ;  but  the  pulley  may  be  made  somewhat  lighter  in  the 
rim,  as  the  conical  form  gives  additional  strength.  In  making  the 
wooden  driver  —  the  iron  pulley  being  furnished  —  the  first  point  is 
to  determine  the  exact  diameter  and  bevel,  for  upon  the  correctness 
of  these,  to  a  great  extent,  depends  the  success  of  the  work. 

To  obtain  these  dimensions,  place  a  square  across  the  smaller  end 


298 


FRICTIONAL,    GEARING. 


of  the  finished  iron  pulley,  and  set  a  bevel  to  it,  as  shown  in  Fig.  81. 

This  will  give  the  correct  bevel  for  the  face  of  the  driver. 

Next,  upon  any  plane 
surface  of  sufficient  size, 
draw  the  lines,  A  B  and 
A  C,  making  the  length 
of  the  line,  A  B,  just 
equal  to  the  larger  diam- 
eter of  the  iron  pulley, 
and  the  angle  at  A  a  right 
angle.  Then,  with  the 
square  and  bevel,  or  with 
a  movable  T  square  ad- 
justed to  the  bevel,  draw 
the  lines  B  C  and  A  D. 


8L 


The  distance,  A  C,  is  the  diameter  required  for  the  driver,  and  the 
other  dimensions  are  easily  obtained. 

To  obtain  the  bevels  for  pulleys  to  work  on  shafts  placed  at  acute 
angles,  draw  the  lines  as  in  the  annexed  diagram,  Fig.  82. 


Fig.  82. 

First,  draw  the  line,  A  B,  to  represent  the  driving  shaft.  Then,  at 
a  right  angle,  draw  the  line  A  C,  making  its  length  equal  to  half  the 
diameter  of  the  driving  pulley.  Next,  at  the  angle  at  which  the 
shafts  are  to  be  set,  draw  the  line  C  D ;  and  at  a  right  angle  from 
this  line,  draw  the  line  C  E,  making  its  length  equal  to  half  the 
required  diameter  of  the  other  pulley.  From  the  point,  E,  parallel 
to  C  D,  draw  the  line  E  F,  which  will  represent  the  other  shaft. 
Now,  from  the  point  of  a  section  of  this  and  the  line  A  B,  draw 
the  line  G  C,  which  will  give  the  bevels  for  both  pulleys. 


FRICTIONAL    GEAKING. 


299 


If  not  above  2J  feet  in  diameter,  the  driver  of  the  bevel  pulleys 
may  be  built  upon  a  "  hub  flange  " —  a  disk  of  iron  of  about  two- 
thirds  the  diameter  of  the  pulley,  with  a  hub  projecting  from  one 
side.  The  hub  should  extend  half  an  inch  beyond  the  thickness  of 
the  wood  to  receive  an  annular  disk  of  smaller  diameter,  through 
which  the  whole  may  be  securely  bolted  together. 

Upon  the  flange,  around  the  hub,  the  pulley  should  be  built.  The 
first  2  or  3  inches,  to  form  the  back,  should  be  of  hard  wood  put  on 
radially.  For  the  balance,  use  soft  maple.  It  is,  in  the  present 
state  of  our  knowledge,  the  only  wood  that  can  be  recommended 
for  this  form  of  friction  gear.  It  should  be  laid  on  this,  as  upon  all 
friction  drivers,  with  the  grain  running  tangentially  as  nearly  as  pos- 
sible. And  each  subsequent  course  should  be  made  smaller,  so  as  to 
form  the  bevel.  The  layers  are  put  together  with  glue  or  white  lead, 
and  carefully  and  thoroughly  nailed.  The  builder  should  be  careful 
to  make  the  joints  perfect,  and  to  put  the  wood  snugly  around  the  hub. 

When  the  wood  is  built  up  to  sufficient  thickness,  the  other  flange 
should  be  put  on,  and  the  whole  bolted  together  and  turned  to  the 
exact  diameter  and  bevel  required,  and  the  pulley  should  be  balanced 
with  the  utmost  care. 

For  a  larger  bevel  driver,  it  is  best  to  use  an  iron  centre  with  arms, 
and  a  flanged  rim  something  like  a  car  wheel.  The  diameter  of  the 
rim  or  cylinder  should  be  a  few  inches  less  than  the  smaller  diameter 
of  the  face  of  the  pulley,  and  that  of  the  flange  something  less  than 
the  larger  diameter.  Upon  this  wheel,  the  wooden  rim  is  built  as 
directed  upon  the  hub  flange,  except  that  the  bolts  must  be  put  in  as 
the  work  progresses,  so  that  subsequent  layers  will  cover  the  heads ; 
and  the  pulley  is  finished  without  the  smaller  flange. 

The  diagram  (Fig.  83)  shows  a  cross  section  of  this  pulley,  which 
will  be  understood  without  further  explanation. 


Fig.  83. 

In  setting  up  this  gearing,  it  is  of  the  utmost  importance  that  the 
countershafts  line  exactly  to  the  centres  of  the  main  or  line  shafts, 
and  at  the  precise  angle  for  which  the  pulleys  were  fitted ;  and  that 
they  are  substantially  set,  so  as  not  to  get  out  of  line. 


300  FRICTIONAL    GEARING. 

This  gearing  is  thrown  on  and  off,  connected  and  separated,  by 
moving  the  countershafts  endwise  in  their  bearings.  This  may  be 
done  by  allowing  the  end  of  the  shaft  to  extend  through  beyond  the 
outer  bearing  far  enough  to  receive  an  extra  box,  one  end  of  which 
is  closed  and  Babbitted  to  receive  the  end  pressure.  This  box  is  set 
up  by  a  lever,  to  which  it  is  pivoted.  And  by  having  the  end  of  the 
shaft  grooved  where  it  is  embraced  by  this  box,  it  will  be  drawn  back 
where  the  lever  is  released.  In  light  work,  it  is  as  well  to  make  the 
outer  bearing  do  the  whole,  by  making  it  both  an  end  and  side  bear- 
ing, and  having  the  box  movable  in  a  line  with  the  shaft. 

The  pressure  required  to  hold  these  pulleys  up  to  the  work  is  not 
great,  and  is  easily  applied  by  finishing  the  end  of  the  shaft,  and 
using  a  flat  bearing  of  anti-friction  metal,  the  full  size  of  the  shaft. 
Sometimes  a  steel  point,  like  a  lathe  centre,  is  set  against  the  end  of 
the  shaft  to  receive  the  pressure ;  but  this  is  a  very  bad  arrangement. 
It  makes  the  bearing  surface  too  small,  and  is  one  of  the  worst  forms 
of  bearing  to  keep  supplied  with  oil.  A  flat  bearing  of  wood,  espe- 
cially of  hard  maple,  is  very  much  better  than  this. 

When  there  is  considerable  difference  in  the  sizes  of  bevel  pulleys 
working  together,  the  end  pressure  is  most  upon  the  shaft  carrying 
the  larger;  but  this  may  frequently  be  neutralized,  upon  lines  having 
several  of  these  drivers,  by  setting  them  with  their  faces  reversed. 

A  point  that  should  never  be  lost  sight  of,  in  constructing  setting 
levers  for  all  friction  work,  is  to  make  them  adjustable,  so  that  the 
pressure  may  be  easily  increased  if  required.  This  is  sometimes  done 
by  a  ratchet  with  several  notches,  into  any  one  of  which  the  lever 
may  be  drawn ;  but  it  is  generally  better  to  have  but  one  catch,  and 
to  make  the  adjustment  elsewhere.  This  may  be  done  by  connecting 
the  lever,  to  the  part  to  be  moved,  by  a  rod  having  adjusting  nuts, 
or  by  making  the  fulcrum  adjustable  by  bolt  or  set  screw. 

These  adjustments  should  be  made  by  the  person  having  charge 
of  the  machinery,  not  by  the  operator  of  each  machine.  They  should 
be  kept  tight  enough  to  do  the  work  required ;  but  more  than  this  is 
a  waste  of  power,  and  a  useless  strain  upon  the  machinery. 

It  may  seem  unnecessary  to  give  the  diagrams  of  lines  for  the 
dimensions  of  bevel  gearing,  as  these  are  well  understood.  But  it 
must  be  remembered  that  we  have  no  work  on  millwrighting  at  pres- 
ent that  gives  information  on  this  point  of  any  scientific  or  practical 
value,  and  that  our  millwrights  are  not  all  familiar  with  the  con- 
struction of  this  gearing.  Our  mills,  though  superior,  are  built  with- 
out rules  or  uniformity  of  construction. 

TlBRA*> 

OK   THK 


-' 


INDEX. 


Abel,  C.  J>.,  on  belting,  8,  48. 
Achard,  A..,  on  rope  transmission,  260. 
Action  of  belting,  130. 
Adhesion,  actual,  no  rule  for,  148. 

of  belting,  18,  49,  105, 108,  111,  131, 147-149, 
161-165. 

of  surfaces.  145,  147,  288. 
Adhesive,  82,  92,  93,  181,  182, 183. 
Advantages  of  belting,  67. 
Albert,  Capt.,  experiment,  13. 
Alexander,  A.,  rule  for  horse-power,  222. 
Alexander  Bros.,  on  belting,  57,  191. 
Allen,  Z.,  on-  shafting,  132. 
«  American  Artisan,"  on  belting,  59,  60. 
Angle  of  belt,  110,  149,  159,  220. 

of  grooved  gear,  77,  80, 164,  285. 
Animal  substances  for  threads,  90. 
Annan,  Wm.,  belt  lacing,  189. 
Apparatus  for  experiments  upon  the  varia- 
tion of  tension,  Morin's,  244. 
Appleton,  American  Cyclopaedia,  84. 

Dictionary  of  Mechanics,  30. 

Mechanics'  Magazine,  48. 

Morin's  Mechanics,  248,  250. 
Aqua  ammonia  for  belts,  183. 
Arc  of  contact,  18,  111,  115,  131,  152,  153,  214, 

218,  221,  225,  226,  242,  243. 
Area,  sectional,  of  belt,  103. 
Arkwright,  8. 

Artnengaud,  Ain6,  on  belting,  124,  129,  164. 
Artnour,  «7.,  power  in  motion,  61. 
Arrangement  of  Table  III.,  246. 
An-esting  and  imparting  motion,  166. 
Association,  N.  E.  Cotton,  132,  149. 
Athenceum  cement,  182. 
Attnospheric  influence  on  the  adhesion  of 

belts,  53, 101. 
Anchincloss  at  Paris  Exposition,  on  belting, 

203. 

Average  tension  or  working  strain  on  belt- 
ing, 13. 
A  ward  to  N.  Y.  Eubber  Co.,  13. 

Babbage  &  Barlow  pulley,  21. 
Babcock  &  Wilcox  on  belting,  96. 
Bacon,  F.  W.,  on  belting,  107, 108, 162, 183. 
Baird,  H.  C.,  86. 
Baker,  8. 
Band  links,  169. 
pulleys,  8. 


Bands,  98.  % 

Band-saw  blades,  strength  of,  9& 
Barbour,  Wm.,  example,  222. 
Barlow  &  Babbage  pulley,  21. 
Barnard,  F.  A.  .P.,  report,  274. 
Bays  denned,  8,  137. 
Beard,  I.  H.,  on  belting,  38,  44,  62. 
Belting  Co.,  N.  Y.,  12. 
Belts,  59,  60,  100. 

action  of,  130. 

adhesion  of,  18,  49,  85,  111,  114, 147, 149. 

advantages  of,  67. 

and  wood  friction  compared,  295. 

angle  of,  110. 

angular,  201,  205. 

average  friction  of,  18. 

best  leather  for,  91,  116,  131. 

big,  24. 

binders,  14, 21,  47, 66,  90, 91, 117, 166, 174, 176. 

breaking  strain  of  leather,  116, 131, 147, 229. 

broad,  197,  202. 

bulky,  64. 

canvas,  97. 

care  of,  38,  46,  47,  58,  82,  114, 124,  196. 

catgut,  90. 

centrifugal  force  of,  150. 

Christie,  J.,  on,  71. 

Claudel's  formula,  13, 14. 

clean,  39,  46,  196. 

Clissold's  patent,  205. 

clutch,  170. 

coarse  loose  leather,  47. 

compared  with  gear,  22,  67,  70,  77,  84. 

compound,  92,  202,  203,  208. 

compressed,  125. 

condition  of,  11,  37,  43,  73. 

contact  of,  rule  for,  18,  93,  95,  112. 

cotton  cord,  275. 

cotton  webbing,  71. 

creep  of,  75. 

crossed.  49,  50,  88,  98,  152,  226. 

disadvantages  of,  67. 

double,  27,  42,  117,  118,  154,  162,  197. 

double  and  single,  50,  73,  82,  92,  93,  117, 
118,  162. 

double  edges,  158,  159,  160,  202. 

dressings  for,  47, 58,  92, 107, 124, 182, 183, 196. 

driving  or  main,  92,  147,  154,  156,  157,  158, 
159,  160,  197,  202. 

driving  power  of,  48,  54,  57, 108, 120, 130. 
301 


302 


INDEX. 


Belts,  edge-bound,  203. 
edge-laid,  197,  209. 
eel-skin,  47,  90. 
elastic,  150. 
elasticity  of,  60. 

examples  of,  19,  24,  25,  27,  28,  29,  30,  31,  33, 
34,  35,  41,  42,  51,  64,  69,  71,  72,  83,  85,  90,  94^ 
95,  96,  107,  118,  120,  154,  157,  158,  160,  190, 
194,  199,  221. 
experiment,  108. 
fan-pulley,  224. 
fastener,  Lincolne's,  186. 
fastenings.    See  Joinings, 
fat  for,  92. 
flat,  68,  98,  89. 
flax,  99. 
flesh-side,  57. 
for  blowers,  73,  74,  224. 
for  centrifugal  machine,  223. 
for  circular  saws,  70. 
for  cooling  shafts,  180. 
for  dies  and  stamp-mills,  170. 
for  driving  fans,  60. 
for  elevator,  12. 
for  high  powers,  101. 
for  rolling-mills,  72,  73,  94,  208,  284. 
for  saws,  119,  173. 
friction,  86. 
frictional  surface,  105. 
gearing,  64. 

good  leather  for,  54,  59,  61. 
grain  side  of,  to  pulley,  19,  49,  50,  54,  56,  57, 

113. 

gum,  12,  59,  92,  97,  98,  150,  157,  193,  197. 
gut,  15,  47,  68,  90,  128,  209. 
gutta-percha,  68,  99,  119,  120,  129. 
Haines's,  205. 
half  cross,  98. 

Hartig,  Dr.,  on  tension  of,  13. 
heavy,  96,  117. 
hemp,  68. 

holding  power  of,  73. 
holes,  180. 
homogeneous,  203. 
hooks,  champion,  185. 

Wilson's,  183,  185. 
horizontal,  46,  92,  148,  149, 153, 196. 
how  not  to  run,  24,  64,  65. 
how  to  clean,  39. 
how  to  get  adhesion,  39. 
how  to  get  regular  speed,  39. 
how  to  oil,  39. 
how  to  run,  25. 
Hunter's  Print- Works,  157. 
impaired,  89. 
inapplicable,  67. 
inclined,  46,  149,  159. 
in  coil,  to  measure,  83. 
India-rubber,  150. 
inextensible,  203. 
intestines,  15. 
in  warm  places,  97. 

joinings,  46, 59, 91, 93, 113, 117, 183-189, 196. 
lacings,  50, 82, 91, 94, 113, 131, 183, 187, 188,189. 


Belts,  laps,  45,  49. 

large,  12,  18,  63,  94,  96, 154. 
larger  than  largest,  12. 
largest,  96. 
leather,  60,  99. 
links,  169. 

long,  43,  46,  62,  88,  153,  196. 
longest,  12,  197. 
loose,  46,  47. 
loss  of  velocity,  88,  89. 
main,  154  to  161,  193-198. 
narrow  vs.  wide,  155. 
new,  73. 

no  definite  rule  for,  149. 
noiseless,  100,  129. 
paper,  187,  198. 
perpendicular,  47,  62,  82. 
philosophy  of,  8,  43. 
pieced  out,  50. 
pitch  line  of,  150. 
pliable,  113,  114. 
ponderous,  64. 
proportion,  43. 
pulleys,  etc.,  60. 
punched  holes  for,  93,  113. 
putting  on,  82,  113,  148. 
quarter-twist,  84,  99,  172-180* 
quick,  44,  46. 
raw-hide,  99,  190. 
riveted  single,  108. 
rosin  on,  47,  89,  105,  108. 
round,  49,  68,  168. 

rubber,  12,  59,  92,  97,  98,  150, 157,  193-197. 
run  to  high  part  of  pulley,  22,  44. 
rules  and  examples  for  horse-power  of,  9, 
13,  17,  18,  19,  26,  27,  28,  29,  30,  31,  32,  33,  34, 
35,  37,  41,  42,  48,  49,  50,  51,  57,  68,  69,  71,  74, 
83,  85,  93,  95, 107, 108, 112, 116, 118, 120, 125, 
131,  152,  155, 156. 157, 159, 161, 196,  207,  208, 
214,  215,  221,  222,  226,  254,  266. 
run  wrong,  64. 
sag  of,  62,  109,  147,  158,  166. 
Sampson's,  207. 
Sanderson's,  204. 
sheet-iron,  151,  190,  204. 
shifter,  51. 
shifting,  98. 
shipping,  19. 

short,  43,  62,  82,  153,  165,  196. 
short-lived,  97. 
single,  27,  93. 
slack,  15,  23,  46,  82,  148. 
sliding  of,  45,  54,  55,  60,  66, 73, 85, 89,  99, 101, 

104,  106,  130,  155,  227,  234,  235. 
slip  df,  49,  54,  55,  60,  66,  73,  85,  89,  90, 101, 104, 

106,  130,  155,  227,  234,  235. 
slow  speed,  144,  145. 
small,  147. 
smooth,  73,  99. 
Spill's,  204. 
splicing,  50. 
steel,  60,  151,  204. 

strain  of,  13,  17, 18,  19,  48,  50,  59,  68,  99,  111, 
130,  131. 


INDEX. 


303 


Belts,  strength  of,  49,  57,  111,  119,  131,  147,  149, 
208,  212,  213,  229. 

stretched  leather,  50,  125. 

stripped,  158,  159,  160. 

strong,  204. 

studs,  Blake's,  184. 

superiority  of,  45. 

surface  contact,  18. 

tensile  strength  of,  9,  13,  14,  17,  40,  48,  61, 
62,  68,  85,  102,  109,  113,  117,  130,  131,  211, 
212,  213,  248. 

theory  of  Frauck,  40. 

thickness  of,  91,  99,  101,  117,  197,  219,  248. 

thin,  93,  128. 

tight,  23,  130,  148. 

tightener,  21,  66,  90,  91. 

to  measure,  15,  111. 

in  coil,  83. 
"  suit  work,  74. 

tool  for  putting  on,  209. 

trapezoidal,  Hoyt's,  205. 

triangular,  201,  205. 

twist  of,  99,  172-180. 

Underwood's  patent,  201. 

unmanageable,  64. 

unpliable,  97. 

varieties  of,  190. 

various  driving,  208. 

vertical,  47.  62,  82,  149,  153. 

vulcanized  rubber,  12,  13,  193. 

water-proof,  200. 

water-proofed,  200. 

Weaver's,  170. 

wet  weather1,  effect  of,  on,  88. 

well-worked,  125. 

well-worn,  73. 

wide,  18,  98,  202. 

wide  vs.  narrow,  155. 

width  of,  111,  125. 

wool,  128,  205. 

work  done  by,  108. 

works  badly,  45. 

woven,  99. 

woven  wire,  204. 

Bennett's  Morin's  Mechanics,  214, 218, 219, 248. 
Berry,  I,.  If.,  on  twist  belt,  173. 
Bevan,  S.,  on  belts,  118. 
Bevan's  experiments,  103. 
Bevel  wheels,  8,  298. 
Blake's  belt-studs,  184. 
Box,  on  mill  work,  7,  119. 
Bi-iggs  &  Towne's  experiments,  214-231. 
Briggs,  Robert,  essay  on  belting,  214. 
Bryant  &  Cogan's  edge-laid  belts,  209. 
Buchanan,  8. 

Buckskin  covered  pulleys,  204. 
Buel,  R.  H.,  on  creep  of  belts,  75. 
Buignet,  binders,  90. 


Cabourg's  machine,  203. 

Calculation  of  sectional  area  of  belting,  103. 

Campbell  &  Co.'s  belts,  156. 

Canvas  belts,  97. 


Care  of  belts,  8,  37,  46,  47,  58,  82,  114,  124,  1%. 
Carillon's  rule  for  horse-power,  125. 
Castor  oil  dressing,  58,  95,  107,  108. 
Catgut  belts,  90. 

Cedar  Point  Iron  Co.,  on  ropes,  276. 
Cements  for  fastening  belts,  181. 

"    pulley  covering,  95,  181. 
Centrifugal  force,  70,  101,  150. 
Chains,  98. 
Champion  belt,  12,  197. 

belt-hook,  185. 

Chasers  cement  for  belts,  181. 
Cheever,  »7.  H.,  gum  belt  experiments,  195. 
Christie,  J".,  on  belts,  71. 
Circular  saw  belts,  119,  173. 
Clarke,  I).  K.,  tables  and  rules,  13,  209. 
Claudel,  on  belts,  13,  14. 
Cleanliness  of  belts,  46. 
Clement,  Benjamin,  on  belts,  95. 
Clissold's  belts,  205. 
Clutch  belts,  170. 
Clutches  of  grooved  gear,  79. 
Coarse,  loose,  leather  belts,  47. 
Coefficient  of  friction,  42,  121,  152,  214,  218. 

"  transformation,  88. 
Colophonium  for  belts,  92. 
Combined  strap-shifter  and  stop  motion,  51. 

fast  and  loose  pulley,  168. 
Communicating  motion  by  belts,  45. 
Comparative  value  of  belts,  97,  204. 
Comparison  of  single  and  doublebelts,117,118. 
Compound  belts,  92,  202,  203,  208. 
Compressed  leather,  125. 
Condition  of  belts,  11,  37,  43,  73. 
Cone  pulleys,  Rankine,  48,  58. 
Cones  of  pulleys,  58. 
Conestoga  Mills'  belts,  154. 
Connected  machinery  by  belts.,  45. 
Connecting  rods,  wire  ropes  as,  285. 

rods  to  transmit  circular  motion,  286. 
Connectors  wrapping,  11,  67. 
Contact  angle  of,  152. 

of  belt  with  pulley,  18,  26,  73,  114,  119,  126, 

127,  149,  151,  152,  214. 
Contents,  16. 
Convexity  of  pulleys,  18,  44,  68,  71,  93,  95,  99, 

105,  110,  153. 

Cooling  shaft  journals,  belts  for,  180. 
Cotton  cord  for  belts,  275. 

spinning,  Leigh's,  22. 

webbing  belts,  71. 
Couch,  A.  B.,  example,  31. 
Coulomb's  rule,  248. 
Covering  for  pulleys,  45,  105,  106, 110, 150, 189, 

204. 

Crafts  &  Filbert's  loose  pulley,  29. 
Crane  Bro.'s  paper  belt,  198. 
Ctirried  leather  belts,  241,  242. 
Curtis,  H.  W.,  on  belts,  158. 


Damp  places,  use  rubber  belts  in,  83. 
Deflection,  or  sag  of  belts  and  ropes,  62, 109, 
256. 


304 


INDEX. 


Designing  belt  gearing,  131. 
Determination  of  the  natural  tension    of 

belting,  232. 

Die  and  stamp-mill  belting,  170. 
Dieterich,  D.  P.,  gum  belts,  193. 
Disadvantages  of  belting,  67. 
Disproportion  of  belting,  45. 
Distance  between  the  shafts  for  belting,  109, 

118. 
Double  and  single  belts,  50, 117, 118. 

belts,  87,  117,  162. 

edge  belts,  158,  202. 

separate  belts.  165. 
Draw  rod  transmission,  267. 
Dressing  for  belts,  47,  58,  92,  107,  124, 181-183, 

196. 
Driving  belts,  superiority  of,  45. 

main,  154,  156,  157, 159, 160, 193, 197,  207,  208. 

power  of  belts,  48,  54,  57,  95,  120,  121, 147. 

pulleys,  well  centred,  100. 
Drums,  immaterial  which  are  driven,  118. 
Duration  of  belts,  27,  59,  85. 
Diirie,  J.,  on  hemp-rope  gearing,  277. 
Dynamics,  law  of,  101. 
Dynamometer  attachments,  243,  251. 


Edge-laid  belting,  197, 209. 
Edivards's,  John,  belts,  128. 
Edwards's  untanned  leather,  209. 
Edivards's,  W.  T.,  belts,  207. 
Eel-skin  bands  and  ropes,  47. 

belting,  47,  90. 

lacings,  183. 
Effect  of  air  on  belting,  53,  101. 

of  eyelets,  50. 

of  slack  on  belting,  15,  148. 

of  speed  OH  belting,  15,  140, 142,  148, 150. 

of  tight  belting,  24, 148. 
Effective  radius  of  pulleys,  59,  98. 
Efficiency  of  belting,  to  increase,  161-165. 
"  Elements  of  Mechanics,"  Nystrom,  35. 
Elephant  hide,  203. 
Elevator  belting,  12. 
Empirical  formulae,  14. 
"  Encyclopaedia    of    Arts,    Manufrs.    and 

Mach.,"  21. 

"  Engineer  and  Machinist's  Assistant,"  8. 
Engineer  on  belts,  93. 
"  Engineer,  The,"  94,  187,  222. 
"Engineering  and  Mining  Journal,"  77. 
"  Engineering  »»  on  raw-hide  belts,  190. 
English  belting,  leather  and  iron  combined, 
204. 

horse-power,  7. 

leather  belting,  207. 

Equal  diameters  and  variable  speed,  150. 
European  compound  leather  belting,  202. 
Examples  of  belts,  19,  24,  25,  27,  28,  29,  30,  31, 
33,  34,  35,  41,  42,  51, 64,  69,  71, 72,  83,  85,  90, 
94,95,96, 107, 118, 120, 154, 157, 158, 160, 190, 
194.  199,  221. 
Experiments  on  belts,  54, 55, 108, 210-213, 232. 

on  the  frictionof  belts  on  wooden  drums,239. 


Experiments  on  the  slipping  of  belts  on  cast- 
iron  pulleys,  238,  241,  242. 

on  the  tension  of  belts,  232. 

on  the  variation  of  tension,  248. 

with  belting,  195. 
Explanations,  5. 
Eyelets,  50. 


Face  of  pulleys,  22,  44,  68,  73,  90,  91,  93,  95,  99, 

105,  110,  153. 

Fairbairn,  on  belting,  8,  67,  222. 
Farey,  J".,  on  steam-engine,  6. 
Fast  and  loose  pulleys,  21,  29,  116,  168. 
Fastening  of  belts,  46,  59,  91,  92,  93, 181-189. 
Fat  for  belts,  92. 

Filberts  &  Craft's  loose  pulley,  29. 
Flanges  to  pulleys,  avoid,  91. 
Flat  face  pulley,  110. 
Flax  belts,  99. 
Flaxen  thread,  90. 
Flexible  pieces,  98. 
Fly-wheel  effects  on  belts,  46. 
Force. required  to  break  belts,  9. 

transmission  by  belts,  214. 

transmitted  by  belts,  9. 

Formula}  for  belts,  13,  19,  25,  102, 103, 108, 112, 
117,  119,  126,  131,  135.  196,  214-225,  232- 
237,  240,  248-251,  266. 
Fpm  denned,  5. 

Franck,  Prof.  I,.  G.,  on  belts,  40. 
Franklin  Inst.  Journal  on  belts,  38, 40,  44,  47, 

48,  66,  205,  214. 

Franklin  Sugar  Refinery  on' belts,  97. 
French  government  agents,  12. 

horse-power,  7. 
Friction  by  adhesion  of  surfaces,  145,  206,  288 

clutch,  170. 

coefficient  of,  152,  214,  218. 

of  belts,  18,  45,  85,  105,  106,  114,  121,  122, 126, 
147,  284. 

of  grain  side  of  belts,  19. 

ratio  of,  115,  126. 

relative  to  arc,  18,  114  119. 

rollers,  162,  165. 

wheels,  145,  206. 
Frictional  gearing,  Robertson,  60,  77. 

gearing,  by  Wicklin,  288. 
Friction  formula,  126. 

of  belts,  experiments  on,  55,  195,  239,  241. 
Fuller's  earth  to  remove  oil,  89. 
Funicular  transmission,  260. 


Gearing,  134, 135,  136. 

compared  with  belts,  22,  67,  70,  77,  84, 118. 

for  mill,  63,  67. 

grooved  clutches,  79. 

horse-power  of,  136. 

table,  136. 

traction,  Hitchcock's  patent,  162. 

treatises  on,  119,  132-135. 
General  statements,  196. 
German  horse-power,  7. 


INDEX. 


305 


Glues  and  cements,  181-183. 

Good  leather  for  belts,  54,  57,  59,  61,  91,  116. 

method  of  lacing,  189. 
Grain  side  of  belting  to  pulley,  19,  49,  50,  54, 

56,  57,  60,  73,  83,  95,  97. 
Gramme  defined,  6. 
Greater  than,  character  to  represent,  5. 
Greek  letters  explained,  5. 
Gregory,  O.,  "  Mechanics,"  207. 
Grooved  friction  gear,  145. 

gear,  77. 

pulleys,  152,  164. 

materials  to  fill,  257,  277. 

speed-ring,  78,  79. 
Gum  belt  (rubber),  12,  59,  92,  97, 98, 150, 157, 193, 

197. 

Gut  (intestines)  belts,  15,  47,  68,  90,  128. 
Gutta-percha  belting,  68,  99,  119,  120,  129. 
Gwynne  &  Co.,  belt  and  friction,  165. 

H nines' s  patent  belt,  205. 
Hair  side  of  belting.    See  Grain  Side. 
Hale,  Kilburn  &  Co.,  belt,  158. 
Harmony  Mill,  Cohoes,  27. 
Hartig,  Dr.,  on  belting,  13. 
Hartman,  J.  M.,  belts,  95. 
Haswell,  on  belting,  30,  48. 
Headless  brass  belt-screws,  203. 
Heavy  belting,  96,  117. 
Heilman,  J"..  rule  for  belting,  126. 
Hemp  ropes,  62,  115,  122,  152,  153,  277-285. 

thread,  90. 

Hepburn  &  Son's  riveted  double  belts,  117. 
Hey  wood,  J.,  belts,  128. 
Hide,  meaning  of,  191. 
High  part  of  pulley,  belt  runs  to,  22,  44. 

velocities,  19,  142. 
Hippopotamus  hide,  203. 
Him,  C.  F.,  on  wire-ropes,  100,  266. 
Hitchcock,  A.,  traction  gearing,  162. 
Hoisting  gear  at  Cincinnati,  51. 
Holding  power  of  belts,  73. 
Holes  for  quarter-twist  belts,  180. 
Hooks,  belt,  183,  185. 
Horizontal  belts,  46,  148,  149,  153,  196. 
Horse-power,  defined,  6,  7. 

English,  French,  German,  Swedish,  Rus- 
sian, 7. 

of  belts  and  examples,  9,  13,  17, 18,  19,  26, 
27,  28,  29,  30,  31,  32,  33,  34,  35,  37,  41,  42,  48, 
49,  50,  51,  57,  68,  69,  71,  74,  83,  85,  93,  95, 107, 
108,  112, 114, 116, 118,  120, 125, 131,  152, 155, 
156,  157,  159,  161, 196,  207,  208, 214,  215,  221, 
222,  226,  254,  266. 

of  gearing,  136. 

table,  136,  139. 

Hors ford's,  E.  N.,  report,  13. 
Howarth  belt  fastener,  187. 
Howe,  I>r.  H.  M.,  on  belting,  97. 
How  not  to  run  belts,  64. 

to  find  the  length  of  a  belt,  15,  111. 

to  use  rubber  belts,  195. 

Hoyt,  J.  B.,  on  belting,  47,  54,  95,  96,  98,  202, 
210,  211,  212. 
20 


Hoyt  &  Co.,  patent  angular  belting,  205. 
Hunebell,  M.,  on  belting,  90. 
Hungarian  leather  lacing,  90. 
Hunter's  Print- Works'  belts,  157. 
Hiittinger,  J.  W.9  translations,  232,  260. 
Hydraulic  connection,  267. 


Illustrations . 

Figs.  1  and  2,  fast  and  loose  pulleys,  21,  22. 

3,  main  driving  belts  for  each  floor,  25. 

4,  Crafts  &  Filbert's  loose  pulley,  29. 

5,  driving  pulley  carrying  two  belts,  34. 

6,  driving  pulley  belt  at  30°,  35. 

7,  strap  shifter  and  stop  motion,  52. 

8,  cones  of  pulleys,  59. 

9,  how  not  to  run  main  belts,  65. 

10,  grooved  speed-ring  and  belt,  79. 

11,  12,  13,  belt  joinings,  92. 

14,  tension  roller,  117. 

15,  pulley,  belt,  and  weights,  121. 

16  and  17,  pulleys,  belts,  and  weights,  123. 

18,  grooved  rope-wheels,  153. 

19,  main  pulley  driving  three  belts,  154. 

20,  main  pulley  driving  two  belts.  155. 

21,  main  pulley  driving  three  belts,  156. 

22,  indicator  card  of  Campbell's  engine,  157. 

23,  driving  belt  at  Hunter's  Print-Works, 
158. 

24,  single  belt  driving  three  shafts,  159. 

25,  driving  belts  of  Patent  Metal  Co.,  161. 

26,  Hitchcock's  traction  gearing,  162. 

27,  Parker's  patent  belting,  163. 

28,  contrivance  to  increase  contact,  163. 

29,  30,  multigrooved  wheels,  164. 

31,  driving  two  shafts  from  one,  165. 

32,  friction  wheel  and  belt,  165. 

33,  double  separate  belts,  166. 

34,  Shaw's  power-hammer  belt,  167. 

35,  36,Shinn's  fast  and  loose  pulley,  168, 169. 
37,38,  band  links,  170 

39,  Weaver's  belting,  171. 

40,  belt  as  friction  clutch,  171. 

41-50,  quarter-twist  belts,  gears,  172-180. 

51,  holes  for  quarter-twist  belts,  180. 

52,  Wilson's  belt-hooks, '184. 

53,  54,  Blake's  belt-studs.  185. 

55,  champion  belt-hook,  186. 

56,  machine-riveted  strapping,  186. 

57,  58,  Lincolne  belt-fastener,  187. 

59,  connecting  the  ends  of  belts,  187. 

60,  lacing  for  paper  belts,  188. 

61,  good  method  of  lacing,  189. 

62,  Alexander  Bros.'  improvement  in  wide 
belting,  191. 

63,  edge-laid  belt,  198. 

64,  65,  Underwood's  patent  angular  belting, 
201. 

66,  tool  for  putting  on  belts,  209. 

67,  side  of  leather  tests,  212. 

68,  diagram  showing  tension  due  to  con- 
tact, 215. 

69,  Morin's  apparatus,  244. 

70,  diagram,  Poncelet's  theory,  249. 


306 


INDEX. 


Illustrations. 

71,  72,  diagrams  showing  sag  of  wire-rope 
256,  257. 

73,  diagram  of  pulley-groove,  258. 

74,  "        of  how  to  avoid  a  high  inclina- 
tion of  wire  ropes,  260. 

75,  diagram  of  rope  transmission,  261. 

76,  77,  diagrams  of  section  of  pulley-groove 

for  wire-rope,  272,  275. 

78,  wire-ropes  as  connecting-rods,  285. 

79,  connecting-rods  for  rotary  motion,  286, 

80,  diagram  of  frictional  gearing  and  belt- 

ing, 294. 
81-83,  diagrams  of  bevel  frictional  gearing, 

298,  299. 

Imparting  and  arresting  motion,  166. 
Inclined  belting,  46,  149,  159. 
Increasing  the  efficiency  of  belting,  161-165. 
InetKtensible  belting,  203. 
Influence  of  thickness  on  belting,  39. 
Intestines  (gut)  for  belting,  15,  47,  68,  90,  128, 

209. 

Iron  and  steel  ropes  compared,  276. 
pulleys,  8,  55,  150. 


Jessup  &  Moore,  on  belting,  96. 
Jewell,  J*.  &  Sons,  on  belting,  96. 
Joinings  of  belt,  46,  59,  91,  113,  117,  183,  184, 

185,  186,  187,  188,  189,  196. 
Journals,  to  cool,  180. 


Kilogramme  defined,  6. 
Kirkaldy's  tests  of  belting,  14. 


Laborde,  M.  E.,  on  belts,  124,  125. 
Lacing  belts,  50,  82,  91,  94,  113, 131,  183,  187, 

188,  189. 

Laps,  disposition  of,  45,  49. 
Large  leather  belts,  12,  18,  63,  94,  96,  154. 
Larger  pulleys,  23. 
Largest  belt  in  the  world,  12,  96. 
Law  of  adhesion,  114, 115, 119, 121, 126, 130, 148, 
149,  226,  242. 

of  coil  adhesion,  116. 
Leather  belting,  compound,  202,  203,  208. 

belting,  good,  54,  59,  61. 

belting,  noiseless,  100,  129. 

best  kind  for  belting,  91,  116,  131. 

compressed  for  belting,  125. 

covered  pulleys,  55,  82,  85,  104,  105,  106,  110, 

189,  204. 

oak- tanned,  57,  58,  91. 

patent  tanned,  109. 

pulley,  77. 

side  of,  tests,  212. 

strength  of,  9, 13,  14,  17,  40,  48,  49, 57,  61, 62, 

68,  102,  111,  113,  117,  119,  130, 131,  147,  149, 

208,  211,  212,  213,  229,  248. 
stretch  of,  58, 117. 
thong,  90. 
Leffel's  "Mechanical  News,"  151. 


Leigh,  Evan,  on  belting,  22-27, 198. 

Leonard's  "Mechanical  Principia,"  118, 196. 

Leroux,  M.,  on  belting,  86. 

Less  than,  character,  5. 

Letters,  Greek,  5. 

Le  Van,  W.  B.,  on  belting,  156,  221. 

Lever, J.  S.,  on  belting,  165. 

Lincolne  belt  fastener,  186. 

Line  upon  line,  49. 

Links,  band,  169. 

Location  of  shafts  and  pulleys,  109. 

Lockwood  &  Co.,  London,  61. 

Logarithm,  5. 

Long  belting,  43,  46,  62,  88,  153,  196. 

Loose  belting,  46,  47. 

and  fast  pulley,  21,  29,  116,  168. 
Loss  of  power  by  axle  friction,  100. 

of  power  by  belting  in  motion,  104. 

of  power  by  slipping  of  belting,  104,  105. 

of  power  in  telodynamic  transmission,  258. 

of  velocity  by  belting  in  motion,  88,  104. 


Machine  riveted  strapping,  186. 
Machinery,  connected  by  belt,  45. 
Machinist,  skilful,  93. 
MacKenzie,  water -proof  composition,   181, 

182. 

Main  driving  belts,  154-161,  193-198. 
Man-power  denned,  6. 
Mason,  John,  rawhide  belt,  190. 
Materials  for  filling  grooves  in  pulleys  for 

wire  ropes,  257. 
Means  of  increasing  the  adhesion  of  belts. 

105,  161-165. 
Measuring  belts,  15,  111. 
Mechanical  News,"  LeffePs,  151. 

"  Principia,"  118,  196. 
'•  Mechanic's  Guide,"  Scholl,  91. 

"  Magazine,"  London,  on  belts,  28, 40, 44, 45, 

187,  205. 
Mechanics  of  belting,  8. 

Overman's,  151. 
Metal,  to  fasten  leather  to,  182. 
Methods  of  transmission  by  belts  and  pulleys, 

154. 

Metre  defined,  6. 
Millimetre  defined,  6. 
Mills  and  Mill-work,  Fairbairn,  67. 
Modulus  of  elasticity,  103. 
Molesworth's  formulae,  31,  44,  181. 
Moore's  rule  for  cement,  183. 
Morin's  data,  6,  7,  14,  17, 18,  41,  44,  48,  88,  99, 

121, 130,  214,  232. 
Moseley,  45. 
Motion,  pulleys  in,  122. 
Mould  on  leather,  to  remove,  182. 


N.  E.  Cotton  Association,  132,  149. 
Neiv  Jersey  Zinc  Co.,  belting,  94. 
Newton's  Journal  on  gear,  77,  275. 
New  York  Belting  Co.,  193. 
Nicholson,  J.,  pulley,  21. 


INDEX. 


307 


Nine  dispositions  of  the  quarter-twist  belt,  172. 

Nobes  &  Hunter  belts,  208. 

Norris  &  Co.'s  belt  tests,  14. 

North  British  Rubber  Co.,  208. 

Note  on  the  sheaves  used  in  the  transmission 

of  power  by  wire  ropes,  275. 
Nothing  like  leather,  77,  211. 
Nystrom,  J.  W.,  on  belting,  35-37. 


Oak-tanned  leather  belts,  57,  81,  91. 

Observations  on  the  results  contained   in 
tables,  240,  242,  246. 

Oil  softens  gum,  98,  196,  197. 

Old  device  to  increase  the  friction  of  cords, 
163, 164. 

On  the  adhesion  of  curried  leather  belts  to 

cast-iron  pulleys,  241,  242. 
the  strength  of  belting  leather,  210. 

"Operative  Mechanic  and  British  Machin- 
ist," 21. 

Oval  punch,  50,  113. 

"  Overman's  Mechanics,"  151. 

Ox-hide,  strength  of,  91,  213. 


Page's  patent  tanned  leather  belts,  109. 
Paper  belting,  187,  198. 

pulleys,  15, 

Parker's  patent  belting,  162. 
Patent  belt  fastenings,  Hoyt  &  Co.'s,  188. 

Metal  Co.'s  belts,  160. 
Pelterau,  display  of  belting,  203. 

belts,  203. 

People's  Works'  gear,  180,  287. 
Period,  5. 

Perpendicular  belting,  47,  62. 
Perrin's  band-saw  blades,  96. 
Philosophy  of  belting,  8. 
Piecing  out  belts,  50. 
"  Polytechnic  Review  "  on  belting,  30, 38,  96. 

"  Centralblatt "  on  belting,  86. 
Poncelet's  theorem,  234,  246,  248. 
Potier's  gut  belting,  209. 
Poullain  Jiros.'  belts,  203. 
Poiver  gained  by  pressure,  114,  126. 

in  motion,  Armour,  61. 

lost  by  friction  of  axle,  100. 

lost  by  shafting,  145. 

transmission  of,  139,  140,  143-148. 
Power-hammer,  Shaw's,  166. 
Practical  Mechanics  of  belting,  9, 115, 124, 729. 

"Mechanics'  Journal"  on  belting,  39,204, 

227,  272. 

"  Praktische  Maschinen  Constructeur,"  104. 
Preller's  leather,  209. 
Pressure  blower  belt,  73. 
Prevention  of  sliding  of  belts,  104. 
Prony's  experiments,  214. 
"Publication  Industrielle"  on  belting,124,164. 
Pulley,  7,  8. 

article  on,  150. 

balanced,  142. 

cones,  48,  58,  84. 


Pulley  contact  for  belting,  18,  73. 

convex,  44,  91,  95,  99,  105,  110,  153. 

covered  with  leather,  55,  58,  82, 85, 104, 105, 
106,  110,  112,  189,  204. 

covered  with  raw  hide,  15. 

covered  with  wood,  105, 150. 

covering,  15,  45, 105, 110. 

effective  radius,  59,  98. 

face,  22,  44,  68,  73,  90,  91,  93,  95,  99,  105,  110, 
153. 

fast  and  loose,  21,  29,  168. 

flanges,  avoid,  91. 

grooved,  152,  153, 163,  164,  168. 

in  motion,  illustrated,  122, 123. 

of  different  diameters,  127. 

of  equal  diameters,  127, 150. 

of  equal  speed,  150. 

of  iron,  8,  55,  150. 

of  leather,  77. 

of  paper,  15. 

of  wood,  55,  91,  150. 

or  wheels  for  wire  rope,  257. 

rounding,  44. 

small,  92. 

smooth  vs.  rough,  125. 

tightening,  14. 

true,  91. 

two,  driven  by  one,  165. 
Punching  belts,  50, 113. 
Punctuation  marks  used,  5. 
Purchasing  belts,  111-113. 
Putting  on  belts,  82,  113, 148. 


Quarter-twist  belts,  84,  99. 172-180. 

holes  for,  180. 
Quick  motion  belts,  44,  46. 


Radius,  effective  for  pulleys,  59, 98. 
Ramsbottom,  on  rope  gearing,  275. 
Rankine,  on  belts,  8,  17,  48,  98,  169,  215,  222. 

on  centrifugal  force,  101. 
Ratio  between  friction  and  traction,  130. 

of  strains,  122. 
Rattier  &  Co.'s  belts,  129. 
Raw-hide  belts,  99,  190. 

pulleys,  15. 

Receipts  of  Spon,  38. 
Regulators  for  mills,  146. 
Relation  of  small  shafting  to  hollow,  132. 
Relative  height  of  wheels,  254. 
Report  of  award  to  New  York  Rubber  Co., 

13. 

Requisites  for  a  belt,  124. 
Resin  on  belts,  47,  89,  105,  108. 
Resistance  to  bending  of  belts,  62. 
Results,  observations  on,  240,  242,  246. 
"Review,  Polytechnic,"  on  belis,  30,  38,  96. 
Richards,  ,T.,  on  belts,  69. 
Richards,  London  &  Kelley,  96. 
Rider,  A.  K.,  on  belts,  116. 
Rigger  defined,  7. 
Right  angles,  shafts  at,  172-178. 


308 


INDEX. 


Rise  of  pulley  face,  90. 
Riveting  belts,  108. 
Robertson,  friction  gear,  60,  77. 
Roebling,  «7.  A.,  on  belts,  51. 

W.  A.,  on  wire  ropes,  253. 
Roller  for  tightening,  14,  21,  47,  66,  90,  91, 117, 

166,  174,  176. 

Rolling-mill  belts,  72,  73,  94,  208,  284. 
Rope-gearing,  cotton,  275. 

"  hemp,  152,  277-285. 

wire,  253-275. 
Rope  of  hemp  or  wire,  62, 115, 122, 152, 153, 204. 

of  steel,  204,  259. 

of  wire  copper,  259. 

slack  of,  256,  257. 

transmission,  253-287. 

vertical,  259. 

Rossman,  C.  R.,  on  belts,  90. 
Round  belts,  49,  68,168. 

Rounding  of  pulleys,  22,  44,  68,  71,  90,  93,  95. 
Rpm,  5. 

Rubber  belts,  12,  59,  92, 97, 98, 150, 157, 193, 197. 
Rule  for  belt  equal  to  gear,  70. 

for  distance  between  shafts,  109. 

for  piecing  out  belts,  50. 

for  sag,  62. 

for  tension  by  weight  of  belt,  62. 

of  thumb,  18. 

to  make  a  double  belt,  191. 
Rules 

for  ascertaining  the  horse-power  of  belts. 
See  Horse-power. 

for  belting  in  coil,  83. 

for  belt  length,  111. 

for  belt  width,  88,  111,  112, 125, 127. 

for  cements  and  leather  dressings,  47,  58, 
92,  107,  124,  181-183,  196. 

for  centrifugal  force,  101. 

for  gearing,  135. 

for  shafting,  137. 
Running  conditions  of  belts,  43. 

off  of  belts,  105. 
Rupture  at  lacing,  50. 
Russian  horse-power,  7. 


Safe  tension  on  belts.    See  Tension. 

Safety  arrangement,  145. 

Sag  of  belts,  62, 109,  147,  158,  166. 

of  ropes,  62,  256. 

Sampson's  patent  belting,  207. 
Sanderson's  patent  belting,  204. 
Saw-belts,  119,  173. 

blades,  band,  strength  of,  96, 151. 
Scellos,  E.,  belts,  203. 
Schenck's  example,  221. 
Scholl,  C.  F.,  on  belting,  91. 
Sectional  area  of  belting,  to  calculate,  103. 
Separate  belts  from  motor,  25. 

double  belts,  165. 
Shafting,  belts  to  cool,  180. 

horse-power  of,  139. 

in  general,  136. 

size  of,  132-140. 


Shafting  tests,  20. 

Shafts  and  pulleys,  location  of,  109. 

at  angle  driven  by  belting,  84,  99, 172-178. 
Shaw's  trip-hammer,  166. 
Sheet-iron  belts,  151,  190,  204. 
Shinn's,  J.,  fast  and  loose  pulley,  168. 
'•  Shoe  and  Leather  Reporter  "  on  belting,  210. 
Shoe-pegs  for  belt-joints,  183. 
Short  belting,  62,  153,  165,  196. 
Side  of  leather,  cut  showing  best  part,  212. 

of  leather,  means,  191. 
Simplicity  desirable,  22. 
Single  and  double  belts,  50,  73,  82,  92,  93,  97, 

109,  117,  118,  162. 

Size  of  band,  way  to  express,  102. 
Skilful  machinist,  93. 
Skin,  eel,  belting,  47. 
Slack  belting,  15,  23,  46,  82,  148. 

of  wire  rope,  256. 
Sliding  (slip),  49, 54, 55, 60,  66,  73,  85,  89,  99, 101, 

104,  106,  130,  155,  227,  234,  235. 
Slip  experiment,  238. 
Slow  shafts,  23. 
Small  pulleys,  92. 
Smithsonian  report,  varnish,  181. 
Smooth  bands,  12,  193. 

faces  desirable,  73. 
Spanish  white  for  belting,  89. 
Special  observations  to  determine  the  natural 

tension  of  belting,  233. 
Speed  cones  (tapering),  48. 

high,  142, 147,  148,  150. 

of  belting,  15,  23,  24,  142,  144,  147,  148,  149. 

slow,  140,  141. 

to  regulate,  146, 147. 

variation  of,  39,  49. 
Speed-ring,  grooved,  79. 
Spier's,  John,  sheet-iron  belt,  190. 
Spill's  patent  belting,  204,  208. 
Splicing  belts,  50. 

wire  rope,  254. 
Spon,  E.,  receipts,  38. 

E.  and  F.  N.,  69, 116,  119, 132. 
S.  S.  Spencer  on  transmission  of  power,  154. 
Steel  belting,  60,  151,  204. 

ropes,  204,  259,  276. 
Stop-motion  and  shifter,  51. 
Strain  on  belting,  9, 13,  17,  18,19,  48,  50,  59,68, 
90,  99,  111,  130,  131,  147,  148,  149,  220. 

on  belting,  effect  of,  89. 
Strapping,  machine-riveted,  186. 
Strap-shifter  and  stop-motion,  51. 
Strength  of  belting,  14,  208,  210-213,  229. 

of  gum,  13. 

of  gutta-percha,  119. 

of  leather,  14,  49,  57,  111,  119, 131,  147,  149, 

208,  210-213,  229. 
Stretch  of  leather,  58,  82,  91. 
Stretched  leather  belting,  50,  54. 
Strips  of  the  cord,  235,  260. 
Sturtevant,  B.  F.,  on  belting,  73. 
Superiority  of  driving  belt,  45, 144. 
Surface  velocity,  10, 13. 
Swedish  horse-power,  7. 


INDEX. 


309 


Sweet,  *T.  JS.,  saw-blades,  96. 
Swell  of  pulley  face,  99. 


Table  for  converting  belt-strain  into  surface 
velocity,  10. 

of  belt  thicknesses,  101. 

of  contents,  16. 

of  driving  power  of  belts,  120. 

of  experiments,  belts  on  cast-iron  pulleys, 
241. 

of  experiments,  beltson  wooden  drums,  239. 

Briggs  &  Towne,  230,  231. 
"  on  belts,  55. 

on  creep  of  belts,  76. 
variation  of  tension,  247. 

of  fan  belts,  74. 

of  formulae  for  belts,  37,  112. 

of  friction  of  ropes  and  belts,  284. 

of  friction  pulley  and  belted  pulleys,  295. 

of  horse-power  of  gears,  136. 
"  shafts,  139. 

of  Kirkaldy's  belt  tests,  14. 

of  metric  measures,  6. 

of  multipliers  per  arc  of  contact,  226. 

of  power  as  per  arc  of  contact,  221,  225. 

of  ratio  of  friction  and  pressure,  127. 

"  "      strains  on  belts,  122. 

of  results  of  belt  tests,  208. 

of  side  of  leather  tests,  212. 

of  slip  of  belts,  89. 

of  strain  as  per  arc  of  contact,  220. 

of  strength  of  belting  leather,  213. 

"  "        saw-blades,  96. 

of  transmission  by  wire  ropes,  255. 

of  units  for  horse-power,  7. 

of  Webber's  shafting  tests,  20. 

of  width  of  belts,  87. 

of  wire  rope  sizes  and  strength,  259. 
Tanners'  dubbing  for  belts,  38. 
Tapering  speed-cones,  48. 
"  Technologist"  on  belting,  90,  107. 
Telodynamic  transmission,  100,  253-275. 
Tensile  strength  of  belting,  9,  13,  14,  17, 40,48, 
61,  62,  68,  85, 102,  113, 117, 130, 131,  208,  210, 
211,  212,  213,  229,  248. 

strength  of  ox-hide,  91,  212,  213. 
Tension  on  belting,  9,  13,  14,  17,  18,  19,  61,  90, 
91,  99,  100,  103,  111,  113, 130,  131,  148,  149, 
220,  232-248. 

that  can  with  safety  be  applied  to  belting, 
248. 

variation  of,  243-251. 
Tests  of  band-saw  blades,  96. 

of  belting,  Centennial  Exhibition,  213. 

of  belting,  Kirkaldy,  14. 

of  shafting,  20. 

Theory  of  belting,  Franck,  40. 
Therefore,  character,  5. 
'I he  science  of  modern  cotton-spinning,  22 
Thickness,  influence  of,  on  belting,  39. 

of  belting,  91,  99,  101,  117,  197,  219,  248. 
Thin  belting,  93,  128. 
Thread  of  hemp  or  flax,  90. 


Thumb  rule,  18. 

Thurston,  Prof.  R.  H.t  on  belting,  48. 
Tight  belting,  effects  of,  24, 148. 
Tightening  (Tension)  roller,  14,  21,  47,  66,  90, 

91,  117,  166,  174,  176. 
To  drive  two  pulleys  from  one,  164. 

fasten  leather  and  cloth  —  glues  and  ce- 
ments, 181-183. 

find  the  horse-power  of  belting.  See  Horse- 
power. 

find  the  length  of  belting,  15,  111. 

find  the  sectional  area  of  belting,  103. 

find  the  strength  of  belting.    See  Strength. 

find  the  width  of  belts,  87,  111,  112, 125, 127, 
149. 

increase  the  efficiency  of  belting,  161-165. 

make  a  double  belt,  191. 

preserve  leather,  181-183. 
Tool  for  putting  on  belts,  208. 
Towne,  S.  R.,  experiments,  8, 215, 218,227-231. 
Traction  gearing,  162. 

of  belts  and  ropes,  18,  130,  260,  261. 
Tractive  force  not  with  area  of  contact,  71. 
Transformation,  co-efficient  of,  88. 
Transmission  by  belts,  128, 129, 131,  143. 

by  cords  and  grooves,  163. 

by  gearing,  133. 

by  hemp  ropes,  122,  152, 153,  277. 

by  wire  ropes,  100,  204,  253-287. 

by  wire  ropes  as  connecting-rods,  285. 

early  modes,  139. 

of  motive  forces  to  a  great  distance,  260. 

of  rotary  motion  by  connecting-rods,  286. 

telodynamic,  Achard,  A.,  260-266. 

telodynamic,  Him,  C.  F.,  100,  266-274. 

telodynamic,  "Manufacturer  and  Builder," 
274. 

telodynamic,  Roebling,  253-260. 
Treatise  on  mechanics,  207. 

on  mill-gearing,  119. 

on  transmission  of  force,  214. 

on  wire-rope  driving,  274. 

on  wood  machinery,  69. 
Treatment  of  belts,  37,  47,  58,  92. 
Twist-belts,  two  or  more  pulleys,  172-180. 


Ultimate  tenacity  of  leather  and  raw  hide, 

100,  131. 

Unclassified  figures  and  notes,  13. 
Underwood's  patent  angular  belt,  201. 
Units  for  horse-power,  7. 

of  measure,  6. 
Untanned  leather  belts,  209. 


Value,  comparative,  of  belts;  97,  204. 

of  greatest  tension  of  wire  rope  and  belts, 

100,  103. 

Van  Nostrand  on  belting,  86. 
Van  Riper,  P.  V.  H.,  on  belting,  81. 
Variation  of  speed,  39,  49,  150. 

of  tension-apparatus,  243,  247-251. 
Varieties  of  belts,  190. 


310 


INDEX. 


Varnish,  elastic,  181. 
Velocity  area  of  belts,  42. 

high,  142,  148,  149. 

low,  140. 

loss  of,  by  belt  in  motion,  88,  90, 104. 

loss  of,  by  various  causes,  89. 

loss  of,  remedied,  89. 

of  surface,  13. 

Verification  of  two  theorems,  etc.,  238. 
Vertical  belts,  47,  62,  82,  149,  153. 

ropes,  259. 


Waterproof  cements,  181-183. 

leather  belting,  200. 
Watt,  Jas.,  on  horse-power,  6. 
Weale  on  belting,  7,  48. 
Weaver's  belting,  170. 
Webber,  Samuel,  on  belting,  17. 
Webber's  tests  of  shafting,  20. 
Webbing,  cotton,  belting,  71. 
Weight  of  belting,  99. 
Welch,  E.  J.  (!.,  on  belting  gearing,  131. 
Wet  weather,  effect  of,  on  belting,  88. 
Wlieels  or  pulleys  for  wire-rope,  257. 


Wheels,  relative  height  of,  254. 

Wicklin  on  friction-gearing,  288. 

Wide  belting,  98. 

Wider  belting  for  certain  machines,  18. 

Width  of  belting,  to  find,  87,  111,  112, 125, 12V 

149. 

Williams,  Jos.,  on  eel-skin  belting,  47. 
Willis,  Prof.,  on  mechanism,  9. 
Wilson's  belt-hook,  183. 
Wire  for  stopping  mill,  146. 

rope,  62,  100,  204,  253-275,  273,  285. 

rope  as  connecting-rods,  285. 

rope,  driving,  274. 

rope,  speed,  100. 

rope,  table,  259. 

woven  belts,  204. 
Wood  friction  bevel  wheels,  298. 

pulleys,  55,  91. 
Wool  belts,  128,  205. 

Work  lost,  due  to  stiffness  of  ropes,  100, 253, 254. 
Working  strain  on  belting,  13,  17, 18, 19, 48f 

50,  59,  99,  111,  119,  131,  229. 
Woven  belting,  99. 
Wrapping  connectors,  67,98. 
Wylde's  circle  of  the  sciences,  115. 


ERRATA. 

On  page  iv.,  for  "  Polytechnic  Journal,"  read  Polytechnic  Review. 

On  cut  No.  37,  complete  the  circle  of  wheel  C. 

Tf  T 
On  page  119,  and  in  original  work  also,  the  expression  —~   in  four  several 

si 

77T    T 

places,  should  take  the  form  of  an  exponent,  thus :   !T=<X  (2.718)  — -;  should 

read  T=t  X  (2.718)^  . 

On  page  165,  fig.  31.    The  lower  pulley  is  A ;  the  middle,  B ;  and  the  upper,  C. 


On  page  217,  line  5  from  top,  should  read  =  1 1  -\-f-  j  . 


In  footnote  to  page  232,  for  "  Let  t  =  natural  tension,  t'  =  t  +  friction  of  belt 
or  drum,"  read,  "  The  sum  of  the  two  tensions  t  and  t'  is  constant,  and,  at  some 
instant  of  the  movement  of  the  drum,  equal  to  the  double  of  the  tension  proper, 
or  natural  T  given  to  each  one  of  the  strips  of  the  belt  in  consequence  of  mov- 
ing the  two  axes  of  rotation  further  apart,  which  is  independent  of  the  action 
of  the  forces  and  of  the  resistances  which  act  upon  the  system.  It  is  clear  that 
we  can  determine  the  constant  and  natural  tension  T,  and  the  tensions  t  and  t', 
relative  to  the  moment  of  slipping.  Knowing,  then,  for  a  same  position  relative 
to  the  two  axes  of  rotation  and  a  same  state  of  the  belt,  the  sums  of  the  two 
tensions,  the  relation  t-\-t'  —  2T,  or  the  double  of  the  natural  tension: ' 


INDEX  TO  ADVERTISEMENTS. 


AMERICAN  OAK-LEATHER  Co.,  LEATHER  BELTING,     .     .     .     .313 

ALEXANDER  BROS.,  LEATHER  BELTING, 314 

THOMAS  WOOD,  FAIRMOUNT  MACHINE  WORKS, 314 

E.  CLAXTON  &  Co.'s  PUBLICATIONS, 315 

Auchincloss's  Practical  Application  of  the  Slide- Valve  and  Link- 

Motion  to  Stationary,  Portable,  Locomotive,  and  Marine  Engines,  315 

Bilgram's  Slide- Valve  Gears, 315 

Cooper's  Treatise  on  the  Use  of  Belting, 315 

Grimshaw  on  Saws, 316 

Hartman  and  Mechener's  Conchology, 316 

Hobson's  Amateur  Mechanic's  Practical  Handbook, 316 

Long  and  Buell's  Cadet  Engineer, 316 

Morton's  System  of  Calculating  Diameter,  Circumference,  Area,  and 

Squaring  the  Circle, 316 

Overman's  Mechanics  for  the  Millwright,  Civil  Engineer,  etc.,    .     .  316 

Riddell's  Carpenter  and  Joiner  Modernized, 317 

Riddell's  New  Elements  of  Hand-Railing, 317 

Riddell's  Mechanic's  Geometry, 317 

Riddell's  Lessons  on  Hand-Railing  for  Learners, 317 

Riddell's  Artisan, 317 

Roper's   Catechism  of  High-Pressure    or    Non-Condensing   Steam- 

Engines, 317 

Roper's  Handbook  of  the  Locomotive, 317 

Roper's  Handbook  of  Land  and  Marine  Engines, 317 

Roper's  Handbook  of  Modern  Steam  Fire-Engines, 317 

Roper's  Engineer's  Handy-Book, 317 

Roper's  Questions  and  Answers  for  Engineers, 317 

Roper's  Use  and  Abuse  of  the  Steam-Boiler, 318 

Sloan's  City  and  Suburban  Architecture, 318 

Sloan's  Constructive  Architecture, 318 

Spang's  Practical  Treatise  on  Lightning  Protection, 318 

Trautwine's  New  Method  of  Calculating  the  Cubic  Contents  of  Ex- 
cavations and  Embankments  by  the  aid  of  Diagrams,       .     .     .     .  318 
Trautwine's  Field  Practice  of  Laying  out  Circular  Curves  for  Rail- 
roads,     ' 318 

Trautwine's  Civil  Engineer's  Pocket-Book, 318 

Webber's  Manual  of  Power  for  Machines,  Shafts,  and  Belts,  .     .     .  318 

White's  Elements  of  Theoretical  and  Descriptive  Astronomy,      .     .  318 

Whitney's  Metallic  Wealth  of  the  United  States, .     ......  318 


THE   LARGEST  OAK   LEATHER  TANNERY  IN   THE  WORLD. 


AMERICAN 

OAK  LEATHER  CO. 

Tanners  and  Manufacturers  of 

"NON  POROUS"  AND  OAK  TANNED 
LEATHER  BELTING, 

DEALERS  IN 

Rubber  Belting,  Hose,  and  Packing, 

Calcutta  Raw-Hide  Lace, 
Patent  Tanned  Lace  and  Mill  Supplies. 

SALESROOM, 

Cor.  Walnut  and  Second  Sts. 

TANNERY  I  Kennar  and  Florence  Sts., 
'  I  Dalton  and   McLean  Aves., 


CHICAGO    BRANCH, 

212  RANDOLPH  STREET. 

ST.  LOUIS   BRANCH, 

404  NORTH  MAIN  STREET. 

(313) 


For  Patent  Double. 


For  Leather  Belting' 


C.  H.  ALEXANDER, 
H.  W.  ALEXANDER, 
E.  P.  ALEXANDER. 


;OST. 
'PHILS.. 

Patentees  and  Manufacturers  of  an  Improvement  in  the  Construction  of 

WIDE  DRIVING  BELTS. 


4IO&4I2 


-For  Description  See  Page  191. 


Ball  and  Socket 
Sclf-Oilinji  Pillow  Block. 


FAIRMOUNT     MACHINE     WORKS. 

Office,  2106  Wood  St.,  Philadelphia. 
T  H  O  3VT  -A.  &     "WOO  3D, 

Manufacture  as  Specialties 

l*o  wer    I.4H  »iii*.    Patent    Bobbin    or    Quill 

Winding?    >B:i«-liin<-.,  Plain  and  Prefer 

i:«-:«mniu  Machines,  Plain  and  Press- 

er    Spooling     Machines,    Keeling, 

Warp  iSplittiiig,  I>yeing,  Sizing, 

Scouring,    Fulling   and    Cal- 

endering Machines, 


16,    18  and  20  yards  Circumference, 

WITH    IMPROVED    HECKS. 

SHAFTING, 

With  Patent 

ADJUSTABLE     SELF-OILING    HAXGERS, 

8,  10,  12,  15,  18,  20,  24  and  30  in.  drop. 

Also   WALL,   POST    AND    GIRDER    HANGERS. 
Pulleys,  from  4  inches  to  10  fVet  in  diameier. 


Pulleys  In  two  parts,  any  size  required. 

PATENT  HOISTING  MACHINES. 
Oil  Presses  Tor  l.ard,  Fi»h  and  Paraffine. 


DEALERS   IN 


COTTON  DUCK 

TENTS-AWNINGS 

RAINPROOF  COVERS 

TWINES  AND  CORDAGE 

MILL  SUPPLIES^ 

FLAGS  AND  BANNERS 

BLOCKS  AND  ROPE 

WIRE  ROPE 


2O2  to  2O8  />  L*  '  1 

South  Water  Street,   OH  ICcl gO,     1 


OFFICE  OF 


THE  JEIIH  LEATHER  BELTING  (J°- 


MANUFACTUBEKS  OF 

— -* — PURE — *- 


OAK  TANNED  LEATHER  BELTING 

324-326-328  PEARL  STREET, 

NEW  YORK. 

APRIL,  1883. 

Have  lately  made  a  Belt  for  the  U.  S.  Electric  Illuminating  Co.  of  N.  Y. 
City,  125  feet  in  length,  and  60  inches  wide,  double;  and  one  for  the  U.  S. 
Warehouse  Co.,  of  Brooklyn,  N.  Y.,  112  feet  in  length,  and  50  inches  wide, 
double;  and,  are  now  making  a  Belt  150  feet  in  length  and  72  inches  wide, 
double,  which  will  be,  when  completed,  the  longest  and  widest  Belt  ever 
made.  The  largest  Belt  known  is  now  running  at  L.  Waterbury  &  Co.'s 
Rope  Manufactory,  Brooklyn,  N.  Y.,  and  was  manufactured  by  the  Heim 
Leather  Belting  Co.  Prize  Medals  received  at  the  Centennial  Exhibition, 
Philadelphia,  1876;  and  at  Chili  Exhibition,  1875;  Berlin,  1877;  Paris, 
1878;  and  American  Institute,  N.  Y.,  1867  to  1881. 


MR.  TRAUTWINE'S  ENGINEERING  WORKS. 


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Civil  Engineer's  Pocket-Book  of  Mensuration,  Trigonometry,  Sur- 
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style,  treats  the  Saw  scientifically,  analyzing  its  action  and  work,  and 
describing,  under  the  leading  classes  of  Reciprocating  and  Continuous 
Acting  Saws,  the  various  kinds  of  large  and  small  Hand,  Sash,  Mulay, 
Jig,  Drag,  Circular,  Cylinder,  and  Band  Saws,  as  now  and  formerly 
used  for  Cross-Cutting,  Ripping,  Scroll- Cutting,  and  all  other  sawing 
operations  in  Wood,  Stone,  and  Metal,  Ice,  Ivory,  etc.,  in  this  coun- 
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1 


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Soiisox.     The    Amateur     Mechanic's     Practical     Hand- 
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LONG  and  BUEL.Ii.— The  Cadet  Engineer,  or  Steam  for  the 
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BUEL,  Assistant  Engineer,  U.  S.  Navy,    Demy  8vo,  cloth.    $2.35. 

MORTON.— The  System  of  Calculating   Diameter,  Circum- 
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MOORE.— The  Universal  Assistant  and  Complete  Mechanic. 
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"VTYSTROM.— A  New  Treatise  on   Elements  of    Mechanics, 

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NYSTROM.— A  New  Treatise  on  Steam  Engineering,  Physi- 
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OVERMAN.  -  Mechanics    for    the    Millwright,    Engineer, 
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OWEN.— Report  of  a  Geological  Survey  of  "Wisconsin.  Iowa, 
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RI DDKLL.— The  Carpenter  and  Joiner  Modernized.  Third 
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accuracy  in  calculation,  showing  it  to  be  indispensable  to  every  workman  in 
giving  the  mensuration  of  surfaces  and  solids,  the  division  of  lines  into  equal 
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RIDDELL.— Mechanic's  Geometry;  plainly  Teaching  the 
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T) I DD ELL.— Lessons   on    Hand-Railing  for  Learners.     By 

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ROPER.— A  Catechism  of  High-Pressure,  or  Non-Condens- 
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ROPER.— Questions  and  Answers  for  Engineers.  This  little 
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3 


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ROPER.— Use  and  A  l»us«>  of  the  Kteam-Roiler.    By  st  ,,>!,,,, 
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edge.    $2.0O.   ,, 

SI,OA  \.    <  il.y  and  Suburban  Architecture.      In  which  are 
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idences, and  Mercantile  Buildings.    By  SAMUEL  SLOAN.    Illustrated  with  131 
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SK,  O  A  N.— Constructive  Architecture.  A  Guide  for  the 
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Five  Orders  of  Architecture ;  selected  from  the  best  specimens  of  Grecian  and 
Roman  art,  with  the  figured  dimensions  of  their  height,  projection,  and  pro- 
file. To  which  is  added  a  treatise  on  Practical  Geometry.  The  whole  illus- 
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Sl»A\<;.-\   Practical  Treatise   on    I  i-Iiiiiin-    Protection. 
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TR  A  ITT  WINE.— A  New  Method    of  Calculating   the   Cubic 
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TRAUTWINE,  C.E.    10  steel  plates.     Sixth  edition,  completely  revised  and 
enlarged.    8vo,  cloth.    $2.OO. 

rpRAIJTWINE.— The  Field  Practice  of  Laying  Out  Circular 

J_  Curves  for  Railroads.  By  JOHN  C.  TRAUTWINE.  C.E.  Eleventh  edition, 
1882,  revised  and  enlarged.  12mo,  tuck.  $2.5O. 

rpRAUT WINE'S  Civil  Engineer's  Pocket-Rook  of  Mensura- 

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and  their  Adjustments,  Strength  of  Materials,  Masonry.  Principles  of  Wooden 
and  Iron  Roof  and  Bridge  Trusses,  Stone  Bridges  and  Culverts,  Trestles, 
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T1TERRER.— A  Manual  of  Power  for  Machines,  Shafts,  and 

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By  SAMUEL  WEBBER,  C.E.  This  work  contains  over  1200  tests,  up  to  date,  of 
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^f  1TIIITE.— The   Elements  of  Theoretical   and   Descriptive 

f  Y  Astronomy,  for  the  use  of  Colleges  and  Academies.  By  CHARLES  J. 
WHITE,  A.M.  Numerous  illustrations,  1  vol.,  demi  bvo.  Fourth  edition, 
revised.  83.OO. 

^ITrHITNEY.-Metallic  Wealth   of   the   United   States,  de- 

YY   scribed  and  compared  with  that  of  other  countries.    By  J.  D.  WHITNEY. 


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